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Painlevéanalysis and analytic solutions of a generalized(3+1)-dimension variable-coefficient nonlinear evolution equation in fluid mechanics and plasma physics 认领 引用
1
作者 Hao-Qing Chen Guang-Mei Wei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2026年第6期14-27,共14页
In this paper,a generalized(3+1)-dimension variable-coefficient nonlinear evolution equation is investigated,which serves as a model for describing nonlinear wave behaviors in shallow water,ion-acoustic wave fluid mec... In this paper,a generalized(3+1)-dimension variable-coefficient nonlinear evolution equation is investigated,which serves as a model for describing nonlinear wave behaviors in shallow water,ion-acoustic wave fluid mechanics and plasma physics.The Painlevéintegrability is tested by the Weiss,Tabor and Carnevale(WTC)method with the simplified form of Krustal.The bilinear form of the equation is derived through the application of the Hirota bilinear method.Building on the bilinear equation,a broad range of analytical solutions are then obtained,including X-shaped and Y-shaped soli ton solutions,lump solution,breather solution,and interaction solutions.In addition,another type of soliton solution,periodic solution,and ratio of trigonometric functions are derived. 展开更多
关键词 (3+1)-dimension nonlinear evolution equation Painlevéintegrability Hirota bilinear method soliton solution lump solution breather solution
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Investigating Solutions in Nonlinear Evolution Equations:A Focus on Local Existence in Mixed Types 认领 引用
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作者 NAFFISA Toureche Trouba FAN Long ABDELGHANI Dahou 《应用数学》 北大核心 2025年第3期691-702,共12页
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe... With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields. 展开更多
关键词 Nonlinear evolution equation Contraction mapping principle Sobolev space Dissipative system
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Extension of Variable Separable Solutions for Nonlinear Evolution Equations 认领 引用 被引量：5
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作者 ZHANG Shun-Li ZHU Xiao-Ning +1 位作者 WANG Yong-Mao LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS 2008年第4期829-832,共4页
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep... We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations. 展开更多
关键词 nonlinear evolution equation variable separable solution generalized conditional symmetry
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A deep learning method for solving third-order nonlinear evolution equations 认领 引用 被引量：13
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作者 Jun Li Yong Chen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第11期19-29,共11页
It has still been difficult to solve nonlinear evolution equations analytically.In this paper,we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly.Specifi... It has still been difficult to solve nonlinear evolution equations analytically.In this paper,we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly.Specifically,the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters.In particular,numerical experiments on several third-order nonlinear evolution equations,including the Korteweg-de Vries(KdV)equation,modified KdV equation,KdV-Burgers equation and Sharma-Tasso-Olver equation,demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well. 展开更多
关键词 deep learning nonlinear evolution equations soliton interaction nonlinear dynamics
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Solving second-order nonlinear evolution partial differential equations using deep learning 认领 引用 被引量：10
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作者 JUN Li Yong Chen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第10期42-52,共11页
Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generat... Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generated from experiments.Specifically,this framework approximates the latent solution with a deep neural network,which is trained with the constraint of underlying physical laws usually expressed by some equations.In particular,we test the effectiveness of the approach for the Burgers'equation used as an example of second-order nonlinear evolution equations under different initial and boundary conditions.The results also indicate that for soliton solutions,the model training costs significantly less time than other initial conditions. 展开更多
关键词 deep learning nonlinear evolution equations data-driven solutions solitons nonlinear dynamics
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Applications of Computer Algebra in Solving Nonlinear Evolution Equations 认领 引用 被引量：18
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作者 XIEFu-Ding GAOXiao-Shan 《Communications in Theoretical Physics》 SCIE CAS 2004年第3期353-356,共4页
With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a res... With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a result, their abundant new soliton-like solutions and period form solutions are found. 展开更多
关键词 computer algebra travelling wave solution nonlinear evolution equation
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Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations 认领 引用 被引量：6
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作者 林万涛 季仲贞 王斌 《Advances in Atmospheric Sciences》 SCIE CAS 2001年第3期413-417,共5页
The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the ... The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001). 展开更多
关键词 Computational quasi-stability Computational stability Forced dissipative nonlinear evolution equation Explicit difference scheme
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Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations 认领 引用 被引量：5
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作者 林万涛 季仲贞 王斌 《Advances in Atmospheric Sciences》 SCIE CAS 2001年第4期604-612,共9页
Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmos... Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated. 展开更多
关键词 Forced dissipative nonlinear evolution equation Explicit quasi-complete square conservative difference scheme Computational stability
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Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation 认领 引用 被引量：6
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作者 XUGui－Qiong LIZhi－Bin 《Communications in Theoretical Physics》 SCIE CAS 2003年第1期39-43,共5页
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbit... A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbitrariness of the manifold in Painlevé analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here. 展开更多
关键词 Painleve analysis rank travelling wave solution nonlinear evolution equation
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A Maple Package on Symbolic Computation of Conserved Densities for (1+l)-Dimensional Nonlinear Evolution Systems 认领 引用 被引量：3
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作者 YANG Xu-Dong RUAN Hang-Yu LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS 2007年第6期961-968,共8页
A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in... A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in removing the redundant terms of the genera/form of the conserved densities but also in solving the conserved densities with the associated flux synchronously without using Euler operator. Furthermore, the program conslaw.mpl can be used to determine the preferences for a given parameterized nonlinear evolution systems. The code is tested on several well-known nonlinear evolution equations from the soliton theory. 展开更多
关键词 conservation laws nonlinear evolution systems computer algebra
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Constructing infinite sequence exact solutions of nonlinear evolution equations 认领 引用 被引量：3
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作者 套格图桑 那仁满都拉 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期23-33,共11页
To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are pr... To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations. 展开更多
关键词 first kind of elliptic function Backlund transformation nonlinear evolution equation new infinite sequence exact solutions
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A New Generalization of Extended Tanh—Function Method for Solving Nonlinear Evolution Equations 认领 引用 被引量：20
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作者 ZHENGXue-Dong CHENYong LIBiao ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS 2003年第6期647-652,共6页
Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equati... Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions. 展开更多
关键词 nonlinear evolution equations exact solutions symbolic computation Riccati equation
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STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS 认领 引用 被引量：1
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作者 YAN Zhen-ya +1 位作者 ZHANG Hong-qing 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第8期925-934,共10页
The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions conta... The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations. 展开更多
关键词 nonlinear evolution equations improved homogeneous balance method exact analytical solution solitary wave solution rational solution
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On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms 认领 引用 被引量：1
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作者 孙杰 路松峰 Samuel L.Braunstein 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第1期22-26,共5页
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimen... In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems. 展开更多
关键词 adiabatic evolution nonlinear evolution paths quantum computing
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The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations 认领 引用 被引量：1
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作者 WU Li-Fei LIN Wan-Tao YANG Xiao-Zhong 《Atmospheric and Oceanic Science Letters》 2011年第5期293-297,共5页
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi... The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations. 展开更多
关键词 nonlinear evolution equation initial perturbations computational stability initial values
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TRAVELLING WAVE SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS BY USING SYMBOLIC COMPUTATION 认领 引用 被引量：7
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作者 Fan Engui E mail:faneg@fudan.edu.cnInstituteofMath.,FudanUniv.,Shanghai200433 《Applied Mathematics(A Journal of Chinese Universities)》 2001年第2期149-155,共7页
A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the par... A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the parameter can be applied in judging the existence of various forms of travelling wave solutions.An efficiency of this method is demonstrated on some equations,which include Burgers Huxley equation,Caudrey Dodd Gibbon Kawada equation,generalized Benjamin Bona Mahony equation and generalized Fisher equation. 展开更多
关键词 Nonlinear evolution equation travelling wave solution symbolic computation.
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A NEW APPROACH TO BACKLUND TRANSFORMATIONSOF NONLINEAR EVOLUTION EQUATIONS 认领 引用 被引量：1
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作者 范恩贵 张鸿庆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第7期645-650,共6页
In this paper, a new approach to Backlund transformations of nonlinear evolution equations is presented. The results obtained by this procedure are completely the same as that by Painleve truncating expansion.
关键词 nonlinear evolution equation Backlund transformation Lax pair
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TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS 认领 引用 被引量：1
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作者 何银年 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期522-529,共8页
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while t... A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution. 展开更多
关键词 nonlinear evolution equation Navier_Stokes equation Taylor expansion method convergence rate
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A Generalized Hirota Ansatz to Obtain Soliton-Like Solutions for a (3+l)-Dimensional Nonlinear Evolution Equation 认领 引用 被引量：1
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作者 吴建平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第8期297-300,共4页
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres... Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived. 展开更多
关键词 （3＋1）-dimensional nonlinear evolution equation bilinear method generalized Hirota ansatz exponential type functions soliton-like solutions
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Generalized Dromion Structures of New(2+1)—Dimensional Nonlinear Evolution Equation 认领 引用 被引量：1
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作者 ZHANGJie－Fang 《Communications in Theoretical Physics》 SCIE CAS 2001年第3期267-270,共4页
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this... We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released. 展开更多
关键词 (2+1) dimensions nonlinear evolution equation soliton dromion
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