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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical periodic Wave solution periodic Cusp Wave solution
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New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 被引量:3
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作者 张文亮 吴国将 +2 位作者 张苗 王军帽 韩家骅 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第4期1156-1164,共9页
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are... In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 展开更多
关键词 auxiliary equation method expanded mapping method (2+1)-dimensional dispersivelong wave equations periodic wave solutions
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Rational and Periodic Solutions for a (2+1)-Dimensional Breaking Soliton Equation Associated with ZS-AKNS Hierarchy 被引量:1
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作者 郝宏海 张大军 +1 位作者 张建兵 姚玉芹 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期430-434,共5页
The double Wronskian solutions whose entries satisfy matrix equation for a (2+1)-dimensional breaking soliton equation ((2+ 1)DBSE) associated with the ZS-AKNS hierarchy are derived through the Wronskian techn... The double Wronskian solutions whose entries satisfy matrix equation for a (2+1)-dimensional breaking soliton equation ((2+ 1)DBSE) associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for (2+1)DBSE are obtained by taking special eases in general double Wronskian solutions. 展开更多
关键词 (2+1)DBSE double Wronskian rational solution periodic solution
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A New Class of Periodic Solutions to (2+1)-Dimensional KdV Equations 被引量:1
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作者 HUANG Wen-Hua LIU Yu-Lu +1 位作者 ZHANG Jie-Fang LAI Xian-Jing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3X期401-406,共6页
We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations... We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations of the periodic solutions to the (2+1)-dimensional KdV equations obtained by means of the Jacobian elliptic function method, but they possess different periods and velocities. 展开更多
关键词 (2+1)-dimensional KdV equation linear superposition periodic solution
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Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional Dispersive Long Wave Equation 被引量:1
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作者 WANGQi CHENYong ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期975-982,共8页
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations.... In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases. 展开更多
关键词 elliptic equation rational expansion method rational form solitary wavesolutions rational form jacobi and weierstrass doubly periodic wave solutions symboliccomputation (1+1)-dimensional dispersive long wave equation
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The Periodic Solitary Wave Solutions for the (2 + 1)-Dimensional Fifth-Order KdV Equation
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作者 Xianghua Meng 《Journal of Applied Mathematics and Physics》 2014年第7期639-643,共5页
The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we invest... The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we investigate the periodic solitary wave solutions for the (2 + 1)-dimensional fifth-order KdV equation by virtue of the Hirota bilinear form. Several novel analytic solutions for such a model are obtained and verified with the help of symbolic computation. 展开更多
关键词 (2 + 1)-Dimensional Fifth-Order KDV Equation periodic SOLITARY Wave solutions HIROTA BILINEAR Form
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Periodic Wave Solutions for(2+1)-Dimensional Boussinesq Equation and(3+1)-Dimensional Kadomtsev-Petviashvili Equation
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作者 ZHANG Huan TIAN Bo +4 位作者 ZHANG Hai-Qiang GENG Tao MENG Xiang-Hua LIU Wen-Jun CAI Ke-Jie 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第11期1169-1176,共8页
For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by... For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by virtueof the Hirota bilinear method and Riemann theta functions,the periodic wave solutions for the(2+1)-dimensionalBoussinesq equation and(3+1)-dimensional Kadomtsev-Petviashvili(KP)equation are obtained.Furthermore,it isshown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions. 展开更多
关键词 periodic wave solutions (2+1)-dimensional Boussinesq equation (3+1)-dimensional KP equation Hirota bilinear method
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New Periodic Wave Solutions and Their Interaction for (2+1)-dimensional KdV Equation
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作者 GE Dong-jie MA Hong-cai YU Yao-dong 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期525-536,共12页
A class of new doubly periodic wave solutions for (2+1)-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution(contain... A class of new doubly periodic wave solutions for (2+1)-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution(contains two arbitrary functions) got by means of multilinear variable separation approach for (2+1)-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions, and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized. 展开更多
关键词 (2+1)-dimensional KdV equation multilinear variable separation approach elliptic functions periodic wave solutions localized excitations interaction property nonelastic completely elastic
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Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio
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作者 Liangwei He Shuanghong Chen 《American Journal of Computational Mathematics》 2021年第4期327-339,共13页
In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation</span><span style="font-size:10pt;font-family:"">... In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">by applying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different </span><span style="font-size:10.0pt;font-family:"">coefficient</span><span style="font-size:10.0pt;font-family:"">s</span><span style="font-size:10pt;font-family:""> <i>p</i>, <i>q</i> and <i>r</i> in the</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">elliptic equation. Then these solutions are</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">coupled into an auxiliary equation</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">and substituted into the (2+1)-dimensional KDV equation. As <span>a result,</span></span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">a large number of complex Jacobi elliptic function solutions are ob</span><span style="font-size:10pt;font-family:"">tained, and many of them have not been found in other documents. As</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10.0pt;font-family:""><span></span></span><span style="font-size:10pt;font-family:"">, some complex solitary solutions are also obtained correspondingly.</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation. 展开更多
关键词 Nonlinear Evolution Equations Jacobi Elliptic Function (2+1)-Dimensional KDV periodic Wave solutions Solitary Wave Solu-tions
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New Multiple Soliton-like and Periodic Solutions for (2+l)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 被引量:3
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作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期793-798,共6页
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ... In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 展开更多
关键词 (2+1)-dimensional canonical generalized (CGKP) equation with variable coefficients tanh function method Riccati equation soliton-like and periodic solutions
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Bifurcations of Exact Traveling Wave Solutions for(2+1)-Dimensional HNLS Equation 被引量:1
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作者 XU Yuan-Fen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第1期68-70,共3页
For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the metho... For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given. 展开更多
关键词 planar dynamical system periodic wave solution solitary wave solution (2+1)-DimensionalHNLS equation
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New Families of Exact Solutions for (2+1)-Dimensional Broer-Kaup System
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作者 ZHAOHong BAICheng-Lin HANJi-Guang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2期251-256,共6页
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soli... Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained. 展开更多
关键词 further modified extended tanh-function method (2+1)-dimensional Broer-Kaup(BK) system soliton-like solutions periodic form solution
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Further Extended Jacobi Elliptic Function Rational Expansion Method and New Families of Jacobi Elliptic Function Solutions to (2+1)-Dimensional Dispersive Long Wave Equation
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作者 ZHANG Yuan-Yuan WANG Qi ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第2期199-206,共8页
In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transf... In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to (2+1)-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations. 展开更多
关键词 doubly periodic solution soliton solution (2+1)-dimensional dispersive long wave equation
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High-dimensional nonlinear variable separation solutions and novel wave excitations for the(4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation
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作者 Zu-feng Liang Xiao-yan Tang Wei Ding 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第11期1-11,共11页
Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresp... Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions. 展开更多
关键词 (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation variable separation solution periodic breathing lumps multi-dromion-ring-type instanton hybrid waves on a doubly periodic wave background
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(4+1)维Fokas方程的有界行波解
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作者 蔡妮平 《成都信息工程大学学报》 2023年第2期240-243,共4页
利用动力系统分岔的方法研究(4+1)维Fokas方程的有界行波解,获得不同参数情况下这个高维方程的行波系统的不同拓扑结构相图.这些相图清楚地展示了行波系统所有可能的有界轨道.通过复杂的椭圆积分,根据这些不同类型的轨道给出有界行波解... 利用动力系统分岔的方法研究(4+1)维Fokas方程的有界行波解,获得不同参数情况下这个高维方程的行波系统的不同拓扑结构相图.这些相图清楚地展示了行波系统所有可能的有界轨道.通过复杂的椭圆积分,根据这些不同类型的轨道给出有界行波解,包括钟型孤立波解和周期波解. 展开更多
关键词 (4+1)维Fokas方程 动力系统 周期波解 孤波解
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On the Quasi-Periodic Wave Solutions and Asymptotic Analysis to a(3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation 被引量:2
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作者 田守富 马潘丽 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第8期245-258,共14页
In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized... In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure. 展开更多
关键词 a(3+1)-dimensional GENERALIZED Kadomtsev–Petviashvili equation Bell’s polynomials Riemann theta function soliton solution periodic wave solution
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On Triply Periodic Wave Solutions for(2+1)-Dimensional Boussinesq Equation 被引量:1
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作者 王军民 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第4期563-567,共5页
By employing Hirota bilinear method and Riemann theta functions of genus one,explicit triply periodic wave solutions for the(2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u =(1... By employing Hirota bilinear method and Riemann theta functions of genus one,explicit triply periodic wave solutions for the(2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u =(1 /6)(u0 1) + 2[ln f(x,y,t)] xx,four kinds of triply periodic wave solutions are derived,and their long wave limit are discussed.The properties of one of the solutions are shown in Fig.1. 展开更多
关键词 Hirota bilinear method theta functions periodic wave solutions (2+1)-dimensional Boussinesq equation
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(3+1)维孤子方程的周期孤波解 被引量:21
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作者 傅海明 戴正德 《东北师大学报(自然科学版)》 CAS CSCD 北大核心 2011年第1期16-19,共4页
扩展了Hirota法,即将Hirota法中的测试函数用新的测试函数来替代,并利用扩展了的方法来构造(3+1)维孤子方程的新的周期孤波解、周期双孤波解、双周期双孤波解.显然扩展的Hirota方法也可以解其他一些非线性发展方程.
关键词 (3+1)维孤子方程 HIROTA方法 周期孤波解 周期双孤波解 双周期双孤波解
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(n+1)维Sinh-Gordon方程新的椭圆函数周期解 被引量:7
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作者 卢殿臣 洪宝剑 +1 位作者 田立新 张大珩 《江苏大学学报(自然科学版)》 EI CAS 北大核心 2007年第6期544-548,共5页
通过引入一个函数变换将(n+1)维Sinh-Gordon方程转化为新的多项式型的非线性偏微分方程.然后由行波约化将其常微分方程化,在拟设法、齐次平衡法和Jacobi椭圆函数法的基础上,借助Mathematica软件和新近提出的F-展开法,求出并研究了(n+1)... 通过引入一个函数变换将(n+1)维Sinh-Gordon方程转化为新的多项式型的非线性偏微分方程.然后由行波约化将其常微分方程化,在拟设法、齐次平衡法和Jacobi椭圆函数法的基础上,借助Mathematica软件和新近提出的F-展开法,求出并研究了(n+1)维SG方程的Jacobi椭圆函数表示的双周期波解,分析了解的结构,在极限情况下这些解退化为相应的孤立波解、三角函数解和奇异行波解.利用数学软件绘出了对应的图形.为进一步研究(n+1)维SG方程在众多的自然科学领域的更广泛的应用提供了理论依据. 展开更多
关键词 (n+1)维Sinh-Gordon方程 F-展开法 周期波解 JACOBI椭圆函数 孤立波解
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用修正的F-展开法求解(n+1)维Sine-Gordon方程 被引量:9
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作者 卢殿臣 洪宝剑 田立新 《兰州理工大学学报》 CAS 北大核心 2007年第1期139-142,共4页
用一个未知函数的变换将(n+1)维Sine-Gordon方程转化为新未知函数及其偏导数为变元的多项式型的非线性偏微分方程.在拟设法、齐次平衡法和Jacobi椭圆函数法的基础上,借助Mathematica软件和修正的F-展开法,求出了(n+1)维SG方程的Weierstr... 用一个未知函数的变换将(n+1)维Sine-Gordon方程转化为新未知函数及其偏导数为变元的多项式型的非线性偏微分方程.在拟设法、齐次平衡法和Jacobi椭圆函数法的基础上,借助Mathematica软件和修正的F-展开法,求出了(n+1)维SG方程的Weierstrass椭圆函数解、Jacobi椭圆函数表示的双周期波解,研究了极限情况下解的退化形式,利用数学软件绘出了部分解对应的图形.研究表明,许多解在欧氏变换下是等价的. 展开更多
关键词 修正的F-展开法 (n+1)维Sine-Gordon方程 周期波解 JACOBI椭圆函数 孤立波解
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