共查询到20条相似文献,搜索用时 25 毫秒
1.
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
2.
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
3.
By using the theory of planar dynamical systems to a coupled non-linear wave equation, the existence of solitary wave solutions and uncountably infinite, many 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. 相似文献
4.
Yongan Xie 《Applied mathematics and computation》2010,217(6):2433-2447
By using the bifurcation theory of dynamical systems, we study the generalized (2+1)-dimensional Boussinesq-Kadomtsev-Petviashvili equation, the existence of solitary wave solutions, compacton solutions, periodic cusp wave solutions and uncountably infinite many smooth periodic wave solutions are 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
5.
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
6.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(11):3402-3417
In this paper, by using the bifurcation theory of dynamical systems for a class of nonlinear fourth order variant of a generalized Camassa–Holm equation, the existence of solitary wave solutions, breaking bounded wave solutions, compacton solutions and non-smooth periodic wave solutions are 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
7.
Bin He Qing Meng Weiguo Rui Yao Long 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2114-2123
Using the method of planar dynamical systems to the mK(n, n) equation, the existence of uncountably infinite many smooth and non-smooth periodic wave solutions, solitary wave solutions and kink and anti-kink wave solutions is proved. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All possible exact explicit parametric representations of smooth and non-smooth travelling wave solutions are obtain. 相似文献
8.
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
9.
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
10.
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
11.
《应用数学年刊》2014,(1)
For the Davey-Stewartson system,the exact dark solitary wave solutions,solitary wave solutions,kink wave solution and periodic wave solutions are studied.To guarantee the existence of the above solutions,all parameter conditions are determined.The persistence of dark solitary wave solutions to the perturbed Davey-Stewartson system is proved. 相似文献
12.
对等离子声波方程, 用平面动力系统理论得到了其光滑、非光滑孤立波解和不可数无穷多光滑、非光滑周期波解的存在性.进一步,在给定的参数条件下,得到了保证上述解存在的充分条件. 相似文献
13.
JiBin Li 《中国科学A辑(英文版)》2008,51(9):1577-1592
Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
14.
By using the bifurcation theory of dynamical systems to modified nonlinear dispersive phi-four equation, we analysis all bifurcations and phase portraits in the parametric space, the existence of solitary wave solutions and uncountably infinite many 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 explicit exact solution formulas are acquired for some special cases. 相似文献
15.
《Chaos, solitons, and fractals》2005,23(2):469-475
Using the method of planar dynamical systems to a higher order wave equations of KdV type, the existence of smooth solitary wave and uncountably infinite many smooth and non-smooth periodic wave solutions is proved. In different regions of the parametric plane, the sufficient conditions to guarantee the existence of the above solutions are given. 相似文献
16.
Jianming Zhang Shuming Li Hongpeng Geng 《Journal of Applied Analysis & Computation》2016,6(4):1205-1210
Using the method of dynamical systems for the the generalized Radhakrishnan, Kundu, Lakshmanan equation, the existence of soliton solutions, uncountably infinite many periodic wave solutions and unbounded wave solution are obtained. Exact explicit parametric representations of the above travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
17.
Aiyong Chen Wentao Huang Shengqiang Tang 《Nonlinear Analysis: Real World Applications》2009,10(5):2659-2665
In this paper, the qualitative behavior and exact travelling wave solutions of the Gilson–Pickering equation are studied by using the qualitative theory of polynomial differential system. The phase portraits of the system are given under different parametric conditions. Some exact travelling wave solutions of the Gilson–Pickering equation are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of smooth and non-smooth travelling wave solutions are given. 相似文献
18.
一类广义四阶非线性Camassa-Holm方程的行波解 总被引:1,自引:1,他引:0
用动力系统的分支理论研究了一类广义四阶非线性Camassa-Holm方程的动力学行为和行波解,发现方程存在一些孤立波解,周期波解和一些诸如Compacton类型的非光滑行波解.在不同的参数条件下,给出了这些解存在的条件和一些特殊条件下的精确解. 相似文献
19.
20.
Hong Li Lilin Ma Kanmin Wang 《Communications in Nonlinear Science & Numerical Simulation》2009,14(8):3296-3304
By using the theory of bifurcations of dynamical systems to the combined k dv–mk dv equation, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. 相似文献