scholarly journals Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions

1998 ◽  
Vol 4 (1) ◽  
pp. 159-191 ◽  
Author(s):  
Y. A. Li ◽  
◽  
P. J. Olver
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Analytic Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Hamiltonian Dynamical System ◽  
Analytic Behavior

scholarly journals Bifurcation of Traveling Wave Solutions of the Dual Ito Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xinghua Fan ◽  
Shasha Li
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Ito Equation

The dual Ito equation can be seen as a two-component generalization of the well-known Camassa-Holm equation. By using the theory of planar dynamical system, we study the existence of its traveling wave solutions. We find that the dual Ito equation has smooth solitary wave solutions, smooth periodic wave solutions, and periodic cusp solutions. Parameter conditions are given to guarantee the existence.

scholarly journals Exact Solutions of Travelling Wave Model via Dynamical System Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Heng Wang ◽  
Longwei Chen ◽  
Hongjiang Liu
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Elliptic Functions ◽  
Wave Model ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Functions ◽  
Wave Solutions ◽  
Periodic Travelling Wave

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. Based on this method, the bounded exact travelling wave solutions are obtained which contain solitary wave solutions and periodic travelling wave solutions. The solitary wave solutions and periodic travelling wave solutions are expressed by the hyperbolic functions and the Jacobian elliptic functions, respectively. The results show that the presented findings improve the related previous conclusions. Furthermore, the numerical simulations of the solitary wave solutions and the periodic travelling wave solutions are given to show the correctness of our results.

scholarly journals Traveling Wave Solutions of a Generalized Zakharov-Kuznetsov Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Wenbin Zhang ◽  
Jiangbo Zhou
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Periodic Solutions ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Planar Dynamical System ◽  
Wave Solutions

We employ the bifurcation theory of planar dynamical system to investigate the traveling-wave solutions of the generalized Zakharov-Kuznetsov equation. Four important types of traveling wave solutions are obtained, which include the solitary wave solutions, periodic solutions, kink solutions, and antikink solutions.

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