Explicit and exact traveling wave solutions of Whitham–Broer–Kaup shallow water equations

2001 ◽  
Vol 285 (1-2) ◽  
pp. 76-80 ◽  
Author(s):  
Fuding Xie ◽  
Zhenya Yan ◽  
Hongqing Zhang
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

scholarly journals Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
M. M. Rashidi ◽  
D. D. Ganji ◽  
S. Dinarvand
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Homotopy Analysis Method ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

On the Exact Traveling Wave Solutions to the van der Waals p-System

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
M. Bilal ◽  
M. Younis ◽  
H. Rezazadeh ◽  
T. A. Sulaiman ◽  
A. Yusuf ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Van Der Waals ◽  
Traveling Wave Solutions ◽  
P System ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250126 ◽  
Author(s):  
FANG YAN ◽  
CUNCAI HUA ◽  
HAIHONG LIU ◽  
ZENGRONG LIU
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Auxiliary Function ◽  
Kp Equation ◽  
Gardner Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kp Equations

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

Bifurcations and Exact Traveling Wave Solutions for a Model of Nonlinear Pulse Propagation in Optical Fibers

2014 ◽  
Vol 24 (06) ◽  
pp. 1450088
Author(s):  
Jibin Li
Keyword(s):  
Optical Fibers ◽  
Traveling Wave ◽  
Pulse Propagation ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Wave System ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Pulse Propagation

In this paper, we consider a model of nonlinear pulse propagation in optical fibers. By investigating the dynamical behavior and bifurcations of solutions of the traveling wave system of PDE, we derive all possible exact explicit traveling wave solutions under different parameter conditions. These results completed the study of traveling wave solutions for the mentioned model posed by [Lenells, 2009].

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