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Exact solutions for the transcritical Riemann problem of two-parameter fluids 认领 引用
1
作者 Haotong BAI Yixin YANG +2 位作者 Wenjia XIE Dejian LI Mingbo SUN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2025年第12期2385-2406,共22页
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad... Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes. 展开更多
关键词 two-parameter fluid Riemann problem(RP) exact solution supercritical fluid pressure splitting transcritical fluid
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Exact solutions of differential equations:renormalization group based polynomial scheme 认领 引用
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作者 Pengfei Guo Yueheng Lan Jianyong Qiao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第10期39-58,共20页
A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most s... A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence,which does not require any sophisticated analysis like Cole-Hopf transformation or Painlevétest.New exact solutions of typical NPDEs are computed with this novel method,including one-and two-soliton(solitary wave)solutions,periodic solutions of exponential or elliptic function type.Moreover,exact reduced equations may also be conveniently computed for further analysis. 展开更多
关键词 polynomial method renormalization group exact solutions
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Exact Solutions of VNE: A Survey 认领 引用 被引量：11
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作者 Haotong Cao Longxiang Yang +1 位作者 Zeyuan Liu Mengting Wu 《China Communications》 SCIE CSCD 2016年第6期48-62,共15页
Network virtualization is an enabling technology of running multiple virtual networks on a shared substrate network. It aims to deal with the ossification of current network architecture. As a crucial component of net... Network virtualization is an enabling technology of running multiple virtual networks on a shared substrate network. It aims to deal with the ossification of current network architecture. As a crucial component of network virtualization, virtual network embedding(VNE) can efficiently and effectively allocates the substrate resource to proposed virtual network requests. According to the optimization strategy, VNE approaches can be classified into three categories: exact, heuristic and meta-heuristic solution. The VNE exact solution is the foundation of its corresponding heuristic and meta-heuristic solutions. This paper presents a survey of existing typical VNE exact solutions, and open problems for the future research of VNE exact solutions are proposed. 展开更多
关键词 network virtualization virtual network requests resource allocation virtual network embedding optimization strategy exact solution
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Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation 认领 引用 被引量：24
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作者 Taogetusang Sirendaoerji 李姝敏 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第6期949-954,共6页
To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki... To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type. 展开更多
关键词 the second kind of elliptic equation Backlund transformation nonlinear evolution equation infi-nite sequence soliton-like exact solution
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Exact solutions of multi-term fractional difusion-wave equations with Robin type boundary conditions 认领 引用 被引量：7
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作者 刘小靖 王记增 +1 位作者 王小敏 周又和 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第1期49-62,共14页
General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solv... General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method. 展开更多
关键词 fractional derivative diffusion-wave equation Laplace transform integraltransform exact solution wavelet
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Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions 认领 引用 被引量：4
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作者 Youtong Zhang Changsong Zheng +2 位作者 Yongfeng Liu Liang Shao Chenhua Gou 《Acta Mechanica Sinica》 SCIE EI CAS 2009年第2期205-210,共6页
This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous exper... This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation. 展开更多
关键词 Exact solution Dual-phase lag Non-Fourier Benchmark solution Heat conduction
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Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations 认领 引用 被引量：12
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作者 QU Gai-Zhu ZHANG Shun-Li ZHU Chun-Rong 《Communications in Theoretical Physics》 SCIE CAS 2008年第5期1119-1124,共6页
The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = ... The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = vxF（u）,uy = vyF（u） }. This approach is also developed to solve （1 ＋ N）-dimensional wave equations. 展开更多
关键词 wave equation invariant set exact solution
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Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach 认领 引用 被引量：7
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作者 高晓楠 杨旭东 楼森岳 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第11期617-622,共6页
Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion... Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosoNic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonie equations are simply obtained for all values of a, Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously. 展开更多
关键词 supersymmetric KdV-a equation bosonization symmetry reductions exact solutions
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Symmetry, Reductions and New Exact Solutions of ANNV Equation Through Lax Pair 认领 引用 被引量：6
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作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS 2008年第7期1-6,共6页
In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, ... In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair. 展开更多
关键词 ANNV equation direct symmetry method Lax pair reductions new exact solutions
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New exact solutions for free vibrations of rectangular thin plates by symplectic dual method 认领 引用 被引量：17
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作者 Yufeng Xing Bo Liu 《Acta Mechanica Sinica》 SCIE EI CAS 2009年第2期265-270,共6页
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-for... The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches. 展开更多
关键词 Classical theory of thin plate Frequency Free vibrations Symplectic dual method Exact solution
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AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL 认领 引用 被引量：4
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作者 YAN Zhenya +1 位作者 ZHANG Hongqing 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期541-546,共6页
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ... Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions. 展开更多
关键词 brusselator reaction model Darboux transformation homogeneous balance method sine-cosine method exact solution
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Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system 认领 引用 被引量：3
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作者 刘萍 曾葆青 +1 位作者 杨建荣 任博 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第1期125-131,共7页
The residual symmetries of the Ablowitz-Kaup-Newell-Segur （AKNS） equations are obtained by the truncated Painleve analysis. The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal r... The residual symmetries of the Ablowitz-Kaup-Newell-Segur （AKNS） equations are obtained by the truncated Painleve analysis. The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system. The local Lie point symme- tries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries, which suggests that the residual symmetry method is a useful complement to the classical Lie group theory. The calcula- tion on the symmetries shows that the enlarged equations are invariant under the scaling transformations, the space-time translations, and the shift translations. Three types of similarity solutions and the reduction equations are demonstrated. Furthermore, several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Backlund transformations between the AKNS equations and the Schwarzian AKNS equation. 展开更多
关键词 residual symmetries Ablowitz-Kaup-Newell-Segur equation exact solution Backlund transformation
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Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length 认领 引用 被引量：5
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作者 Y Chargui L Chetouani A Trabelsi 《Chinese Physics B》 SCIE EI CAS 2010年第2期43-47,共5页
Using the momentum space representation, we solve the Klein--Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterize... Using the momentum space representation, we solve the Klein--Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained. 展开更多
关键词 Klein--Gordon equation linear potential minimal length exact solution
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Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model 认领 引用 被引量：2
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作者 陈星 张振伟 +3 位作者 赵环 王暖让 杨仁福 冯克明 《Chinese Physics Letters》 SCIE EI CAS CSCD 2016年第10期62-66,共5页
We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin spin interaction and transverse field model. The collective spin noises at any time are... We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation. 展开更多
关键词 of on for in Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model is
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Finite Symmetry Transformation Groups and Some Exact Solutions to(2+1)-Dimensional Cubic Nonlinear Schrdinger Equantion 认领 引用 被引量：5
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作者 LI Biao LI Yu-Qi CHEN Yong 《Communications in Theoretical Physics》 SCIE CAS 2009年第5期773-776,共4页
Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cyl... Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution. 展开更多
关键词 symmetry groups cubic NLS equation exact solution
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Symmetries and Exact Solutions of the Breaking Soliton Equation 认领 引用 被引量：9
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作者 陈美 刘希强 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第11期851-855,共5页
With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usi... With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations. 展开更多
关键词 breaking soliton equation symmetry similarity reductions exact solutions
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An application of interacting shear flows theory: exact solution for unsteady oblique stagnation point flow 认领 引用 被引量：4
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作者 Guibo Li Minguo Dai Z. Gao 《Acta Mechanica Sinica》 SCIE EI CAS 2006年第5期397-402,共6页
An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS... An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented. 展开更多
关键词 Navier-Stokes equations Interacting shear flows Unsteady oblique stagnation point flow Exact solution
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EXACT SOLUTIONS FOR FREE VIBRATION OF TRANSVERSELY ISOTROPIC PIEZOELECTRIC CIRCULAR PLATES 认领 引用 被引量：4
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作者 丁皓江 徐荣桥 陈伟球 《Acta Mechanica Sinica》 SCIE EI CAS 2000年第2期141-147,共7页
By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. ... By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. 展开更多
关键词 exact solution piezoelectric circular plate free vibration
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Lie Symmetry Analysis,Bcklund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations 认领 引用 被引量：3
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作者 刘汉泽 李继彬 刘磊 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第5期737-742,共6页
This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,th... This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations. 展开更多
关键词 （2＋1）-dimensional Burgers＇ equation heat equation Lie symmetry analysis Bcklund transformation optimal system exact solution
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Coupled Nonlinear Schrodinger Equation: Symmetries and Exact Solutions 认领 引用 被引量：7
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作者 LIU Ping LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS 2009年第1期27-34,共8页
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr... The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries. 展开更多
关键词 coupled nonlinear SchrSdinger equation classical Lie group approach symmetry exact solution
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