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1.
The traveling wave solutions of the magma equation are studied by using the approach of dynamical systems and the theory of bifurcations. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. Under different regions of parametric space, various sufficient conditions to guarantee the existence of solitary wave, periodic wave and breaking wave solutions are given. Moreover, the reason for appearance of breaking waves is explained. 相似文献
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Tang Shengqiang Huang Wentao 《高校应用数学学报(英文版)》2007,22(1):21-28
In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained. 相似文献
3.
By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed. 相似文献
4.
利用动力系统的Hopf分支理论来研究耦合非线性波方程周期行波解的存在性和稳定性.应用行波法把一类耦合非线性波方程转换为三维动力系统来研究,从而给在不同的参数条件下给出了周期解存在和稳定性的充分条件. 相似文献
5.
Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model
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A long waves-short waves model is studied by using the approach of dynamical systems. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of the parametric space are given. All possible explicit exact parametric representations of above traveling waves are presented. When the energy of Hamiltonian system corresponding to this model varies, we also show the convergence of the periodic wave solutions, such as the periodic wave solutions converge to the solitary wave solutions,
kink and anti-kink wave solutions, and periodic wave solutions, respectively. 相似文献
6.
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived. 相似文献
7.
The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that thes... 相似文献
8.
Jaulent-Miodek方程的行波解分支 总被引:1,自引:0,他引:1
利用平面动力系统分支理论研究了耦合的Jaulent-Miodek方程的孤立波及周期波的存在性,求出了分支参数集.在给定的参数条件下,得到了该方程光滑孤立波解及周期行波解的所有可能的显式表达式. 相似文献
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10.
Shengqiang Tang Xiaoliang Huang Wentao Huang 《Applied mathematics and computation》2010,216(10):2881-2890
By using the bifurcation theory of dynamical systems to the generalized Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation, the existence of solitary wave solutions, compactons solution, non-smooth periodic cusp wave solutions and uncountably infinite many smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined. 相似文献
11.
The traveling wave solutions of the generalized nonlinear derivative Schrödinger equation and the high-order dispersive nonlinear Schrödinger equation are studied by using the approach of dynamical systems and the theory of bifurcations. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. All possible explicit parametric representations of the bounded traveling wave solutions (solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions) are given. 相似文献
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The Exact Solutions of Generalized Zakharov Equations with High Order Singular Points and Arbitrary Power Nonlinearities
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Zhenxing Chen Huifang Wei Zhaofu Luo Longwei Chen 《Journal of Applied Analysis & Computation》2016,6(3):884-892
In this paper, we using bifurcation theory method of dynamical systems to find the exact solutions of generalized Zakharov equations with high order singular points and arbitrary power nonlinearities. Under different parameter conditions, we obtain exact solitary wave solutions, periodic wave solutions as well as kink and anti-kink wave solutions. 相似文献
14.
By using the method of planar dynamical systems to an integrable nonlinear wave equation, the existence of periodic travelling wave, solitary wave and kink wave solutions is proved in the different parametric conditions. The phase portraits of the travelling wave system are given. It can be shown that the existence of singular curves in the travelling wave system is the reason why the travelling wave solutions lose their smoothness. Moreover, the so-called W/M-shaped solitary wave solutions are obtained. 相似文献
15.
获得了广义的Zakharov方程和Ginzburg-Landau方程的一些精确行波解,这些行波解有什么样的动力学行为,它们怎样依赖系统的参数?该文将利用动力系统方法回答这些问题,给出了两个方程的6个行波解的精确参数表达式. 相似文献
16.
Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations
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In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions. 相似文献
17.
Fang Yan Haihong Liu Zengrong Liu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):2824-2832
By using methods from dynamical systems theory, this paper researches the bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation. Implicit exact parametric representations of all travelling wave solutions as well as some explicit analytic solutions are given. Specially, breaking wave solutions are obtained, which KdV equation does not include. 相似文献
18.
Bifurcation of travelling wave solutions for (2+1)-dimension nonlinear dispersive long wave equation
In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for (2+1)-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed. 相似文献
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Weiqin Yu Na Li Fangqi Chen Shouwei Zhao 《Journal of Applied Analysis & Computation》2016,6(4):968-980
Utilizing the methods of dynamical system theory, the Dullin-Gottwald-Holm equation is studied in this paper. The dynamical behaviors of the traveling wave solutions and their bifurcations are presented in different parameter regions. Furthermore, the exact explicit forms of all possible bounded solutions, such as solitary wave solutions, periodic wave solutions and breaking loop wave solutions are obtained. 相似文献