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Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method 认领 引用
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作者 刘春平 林支桂 《Communications in Theoretical Physics》 SCIE CAS 2010年第11期781-784,共4页
First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear ... First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method. 展开更多
关键词 modified extended tanh-function method travelling wave solution a class of nonlinear waveequation hyperbolic-function method
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Auto-Backlund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation 认领 引用
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作者 Rehab M. El-Shiekh 《American Journal of Computational Mathematics》 2015年第2期215-223,共9页
In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Ca... In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients. 展开更多
关键词 Auto-Backlund Transformation Homogeneous Balance Method The Extended Tanh-Function Method The Time-Dependent Coefficients Calogero-Degasperis Equation Exact Solutions
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Generalized Extended tanh-function Method for Traveling Wave Solutions of Nonlinear Physical Equations 认领 引用 被引量：6
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作者 CHANG JING GAO YI-XIAN AND CAI HUA 《Communications in Mathematical Research》 CSCD 2014年第1期60-70,共11页
In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher＇s equation, the nonlinear schr＆#168;odinger equat... In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher＇s equation, the nonlinear schr＆#168;odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics. 展开更多
关键词 generalized tanh-function method nonlinear Schrodinger equation,Fisher＇s equation
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Extended Complex tanh-Function Method and Exact Solutions to (2+1)-Dimensional Hirota Equation 认领 引用 被引量：1
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作者 ZHAO Hong 《Communications in Theoretical Physics》 SCIE CAS 2007年第2期200-202,共3页
In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is mo... In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple. 展开更多
关键词 nonlinear equations symbolic computation extended complex tanh-function method exact solutions
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Adaptive optimal tracking control for underactuated surface vessels using extended state observer and reinforcement learning 认领 引用
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作者 Yinkun Li Yawen Zhou +1 位作者 Yufeng Zhou Li Chai 《Journal of Automation and Intelligence》 EI CSCD 2026年第1期24-34,共11页
This paper investigates the adaptive optimal tracking control(AOTC)for underactuated surface vessels(USVs).Compared to the majority of existing studies,the control strategy in this paper innovatively combines an exten... This paper investigates the adaptive optimal tracking control(AOTC)for underactuated surface vessels(USVs).Compared to the majority of existing studies,the control strategy in this paper innovatively combines an extended state observer(ESO)with reinforcement learning(RL).The designed ESO has high estimation accuracy and robust disturbance rejection capabilities for the unmeasurable information for USVs.To obtain the AOTC,the actor–critic(AC)networks based on RL are constructed to solve the Hamilton–Jacobi–Bellman(HJB)equations.Due to the uncertainties,it is challenging to obtain the optimal controller by directly solving the HJB equations.To address this issue,this paper employs neural networks(NNs)to approximate the uncertainties and solves the optimal controller via AC-RL and ESO.In addition,the adaptive parameters of the optimal controller is trained in parallel with AC networks,which can ensure that the trained networks can further improve tracking performance.The boundedness of AOTC for USVs is shown by Lyapunov stability theorem.Finally,simulation results demonstrate the effectiveness of the proposed algorithm. 展开更多
关键词 Extended state observer Actor–critic networks Reinforcement learning Backstepping method Underactuated surface vessel
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Extended multiscale finite element method for mechanical analysis of heterogeneous materials 认领 引用 被引量：9
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作者 Hong-Wu Zhang Jing-Kai Wu +1 位作者 Jun Lv Zhen-Dong Fu 《Acta Mechanica Sinica》 SCIE EI CAS 2010年第6期899-920,共22页
An extended multiscale finite element method(EMsFEM)is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscal... An extended multiscale finite element method(EMsFEM)is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials,the construction methods of the base functions for continuum heterogeneous materials are systematically introduced.Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions,thus,different kinds of boundary conditions are proposed.The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also,a consistency test of the method is performed numerically.The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions. 展开更多
关键词 Extended multiscale finite element method Heterogeneous material Base function Downscaling computation
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Soliton molecules and the CRE method in the extended mKdV equation 认领 引用 被引量：4
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作者 Bo Ren Ji Lin Ping Liu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第5期41-45,共5页
The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition,which is called velocity resonance.One soliton molecule and interaction between ... The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition,which is called velocity resonance.One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters.The soliton molecules including the bright and bright soliton,the dark and bright soliton,and the dark and dark soliton are exhibited in figures 1–3,respectively.Meanwhile,the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevémethod.The consistent Riccati expansion(CRE)method is applied to the extended mKdV equation.It demonstrates that the extended mKdV equation is a CRE solvable system.A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method. 展开更多
关键词 extended mKdV equation soliton molecule CRE method nonlocal symmetry
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The extended auxiliary the KdV equation with equation method for variable coefficients 认领 引用 被引量：12
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作者 Shi Lan-Fang Chen Cai-Sheng Zhou Xian-Chun 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第10期166-170,共5页
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational funct... This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics. 展开更多
关键词 extended auxiliary equation method KdV equation with variable coefficients exactsolutions
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Fracture properties of epoxy asphalt mixture based on extended finite element method 认领 引用 被引量：10
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作者 钱振东 胡靖 《Journal of Central South University》 SCIE EI CAS 2012年第11期3335-3341,共7页
Crack is found to be a major distress that affects the performance of the epoxy asphalt pavement.An extended finite element method was proposed for investigating the fracture properties of the epoxy asphalt mixture.Fi... Crack is found to be a major distress that affects the performance of the epoxy asphalt pavement.An extended finite element method was proposed for investigating the fracture properties of the epoxy asphalt mixture.Firstly,the single-edge notched beam test was used to analyze the temperature effect and calculate the material parameters.Then,the mechanical responses were studied using numerical analysis.It is concluded that 5℃ can be selected as the critical temperature that affects the fracture properties,and numerical simulations indicate that crack propagation is found to significantly affect the stress state of the epoxy asphalt mixture.The maximum principal stress at the crack surface exhibits different trends at various temperatures.Numerical solution of stress intensity factor can well meet the theoretical solution,especially when the temperature is lower than 5℃. 展开更多
关键词 epoxy asphalt mixture microstructure extended finite element method fracture morphology mechanical response
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An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass 认领 引用 被引量：11
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作者 L.F.Fan F.Ren G.W.Ma 《Journal of Rock Mechanics and Geotechnical Engineering》 2011年第1期73-81,共9页
An extended displacement discontinuity method(EDDM)is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass(VRM).The discontinuities in a rock mass are divided into two groups.The primary g... An extended displacement discontinuity method(EDDM)is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass(VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass(ERM)from the conventional displacement discontinuity method(CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored. 展开更多
关键词 stress wave propagation extended displacement discontinuity method(EDDM) viscoelastic rock mass(VRM) micro-defect macro-joint
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Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method 认领 引用 被引量：4
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作者 郑安兴 罗先启 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第11期4337-4346,共10页
The extended finite element method(XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that ... The extended finite element method(XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that remeshing for moving discontinuities can be overcome. The extended finite element method is presented for hydro-mechanical modeling of impermeable discontinuities in rock. The governing equation of XFEM for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface. The coupling relationship between water pressure gradient on crack surface and fracture opening width is obtained by semi-analytical and semi-numerical method. This method simplifies coupling analysis iteration and improves computational precision. Finally, the efficiency of the proposed method for modeling hydraulic fracture problems is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed. 展开更多
关键词 extended finite element method crack hydraulic fra
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Real-time embedded software testing method based on extended finite state machine 认领 引用 被引量：10
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作者 Yongfeng Yin Bin Liu Hongying Ni 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第2期276-285,共10页
The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliab... The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliability. Based on the analysis of the characteristics of real-time embedded software, the formal method is introduced into the real-time embedded software testing field and the real-time extended finite state machine （RT-EFSM） model is studied firstly. Then, the time zone division method of real-time embedded system is presented and the definition and description methods of time-constrained transition equivalence class （timeCTEC） are presented. Furthermore, the approaches of the testing sequence and test case generation are put forward. Finally, the proposed method is applied to a typical avionics real- time embedded software testing practice and the examples of the timeCTEC, testing sequences and test cases are given. With the analysis of the testing result, the application verification shows that the proposed method can effectively describe the real-time embedded software state transition characteristics and real-time requirements and play the advantages of the formal methods in accuracy, effectiveness and the automation supporting. Combined with the testing platform, the real-time, closed loop and automated simulation testing for real-time embedded software can be realized effectively. 展开更多
关键词 real-time system real-time embedded software for- mal method extended finite state machine （EFSM） testing se- quence test case.
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Numerical Study of Quasi-Static Crack Growth Problems Based on Extended Finite Element Method 认领 引用 被引量：3
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作者 郑安兴 罗先启 《Journal of Shanghai Jiaotong university(Science)》 EI 2014年第6期736-746,共11页
The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor... The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor(SIF) are discussed,and the proper parameters to calculate the SIF are given. The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size, and the crack path is not mesh-sensitive. A reanalysis method for the XFEM has been introduced. The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases. 展开更多
关键词 extended finite element method(XFEM) stress intensity factor(SIF) crack level set numerical methods
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Spatial differences of exergy use of cement manufacturing industry in China based on extended exergy accounting method 认领 引用 被引量：1
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作者 CHEN Fengnan SHEN Lei +1 位作者 LIU Litao GAO Tianming 《Journal of Geographical Sciences》 SCIE CSCD 2015年第11期1393-1407,共15页
Factory-level data from 23 provinces and some national statistical data in cement manufacturing industry and socio-economies in 2012 are used to analyze the spatial distribution of exergy use for China＇s cement manuf... Factory-level data from 23 provinces and some national statistical data in cement manufacturing industry and socio-economies in 2012 are used to analyze the spatial distribution of exergy use for China＇s cement manufacturing industry by the Extended Exergy Accounting method. This method takes full account of the inclusion of energy and raw material supply and other external factors （capital, labor and environment） into a comprehensive resource cost assessment. The extended exergy consumption and its intensity quantitatively at the provincial levels of cement production were calculated and then the agglomeration level of exergy use at the regional level was also evaluated. Based on this analysis, their spatial difference in size and efficiency of exergy use at the provincial level were identified. Moreover, their regional characteristics were revealed. Some important results could be drawn as follows. First, the invisible social cost accounted for 1/10 of the total exergy use in cement manufacturing industry, while the energy element shared about 9/10. Second, the gross distribution of exergy use in China＇s cement manufacturing industry was mainly concentrated in the eastern region like Anhui and Shandong provinces, and in the western region like Sichuan province. In terms of exergy use, the coal and electricity were the highest of energy costs in the eastern region, whereas the cost of capital, labor and external environmental factors highlighted the invisible social cost for cement production in the central and western regions to some extent. Third, the efficiency distribution of exergy use in China＇s cement manufacturing industry illustrated an incremental feature from west to east, especially for the energy, labor and capital efficiencies. An evaluation on the environmental efficiency indicated that provinces or regions like Tibet, Xinjiang, Inner Mongolia and Shanxi have undertaken much higher environmental costs. Fourth, the 23 provinces could be classified into eight groups by the Euclidean distance model using the gross and efficiency results of exergy use. Fifth, the high industry concentration degree is the main driving factor of exergy efficiency improvement for cement manufacturing industry in China. 展开更多
关键词 cement manufacturing industry spatial difference exergy use extended exergy accounting method
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Evaluation of mixed-mode stress intensity factors by extended finite element method 认领 引用 被引量：3
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作者 茹忠亮 赵洪波 尹顺德 《Journal of Central South University》 SCIE EI CAS 2013年第5期1420-1425,共6页
Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function... Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient. 展开更多
关键词 stress intensity factor （SIF） interaction integral method extended finite element method （XFEM）
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Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method 认领 引用 被引量：1
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作者 WANG Xiang-nan YU Peng +4 位作者 ZHANG Xiang-tao YU Jia-lin HAO Qing-shuo LI Quan-ming YU Yu-zhen 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第1期235-246,共12页
In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination... In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously. 展开更多
关键词 extended finite element method crack three-dimensional calculation cracking potential function tensile failure
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A numerical method for determining the stuck point in extended reach drilling 认领 引用 被引量：2
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作者 Sun Lianzhong Gao Deli 《Petroleum Science》 SCIE CAS CSCD 2011年第3期345-352,共8页
A stuck drill string results in a major non-productive cost in extended reach drilling engineering.The first step is to determine the depth at which the sticking has occurred.Methods of measurement have been proved us... A stuck drill string results in a major non-productive cost in extended reach drilling engineering.The first step is to determine the depth at which the sticking has occurred.Methods of measurement have been proved useful for determining the stuck points,but these operations take considerable time.As a result of the limitation with the current operational practices,calculation methods are still preferred to estimate the stuck point depth.Current analytical methods do not consider friction and are only valid for vertical rather than extended reach wells.The numerical method is established to take full account of down hole friction,tool joint,upset end of drill pipe,combination drill strings and tubular materials so that it is valid to determine the stuck point in extended reach wells.The pull test,torsion test and combined test of rotation and pulling can be used to determine the stuck point.The results show that down hole friction,tool joint,upset end of drill pipe,tubular sizes and materials have significant effects on the pull length and/or the twist angle of the stuck drill string. 展开更多
关键词 Extended reach drilling stuck pipe torque and drag numerical method
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Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method 认领 引用 被引量：3
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作者 朱振泱 CHEN Weimin ZHANG Guoxin 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2017年第5期1132-1139,共8页
Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete cr... Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation. 展开更多
关键词 concrete crack self-deformation loads extended finite element method
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Applying the New Extended Direct Algebraic Method to Solve the Equation of Obliquely Interacting Waves in Shallow Waters 认领 引用 被引量：1
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作者 KURT Ali TOZAR Ali TASBOZAN Orkun 《Journal of Ocean University of China》 SCIE CAS CSCD 2020年第4期772-780,共9页
In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study... In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field. 展开更多
关键词 conformable fractional derivative new extended direct algebraic method interacting wave equation shallow water waves
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On a Generalized Extended F-Expansion Method 认领 引用 被引量：3
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作者 REN Yu-Jie LIU Shu-Tian ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS 2006年第1期15-28,共14页
Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generali... Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the （2＋1）-dimentional breaking soliton equation. As a result, we successfully obtain some new and more general solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sampler the properties of some soliton solutions for the breaking soliton equation are shown by some figures. Our method can also be applied to other partial differential equations. 展开更多
关键词 （2＋1）-dimentional breaking soliton equation generalized extended F-expansion method Jacobi elliptic function solution generalized ansatz soliton-like solution
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