Exact traveling wave solutions of some nonlinear physical models. II. Coupled KdV type equations

2000 ◽  
Vol 5 (4) ◽  
pp. 162-169
Author(s):  
Jianlan Hu ◽  
X. Feng ◽  
Zhi Li
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Physical Models ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kdv Type Equations

scholarly journals Ion-Acoustic Solitary Wave Solutions of Three-Dimensional Zakharov-KuznetsovBurgers Equation for Dust Ion Acoustic Waves and Their Applications

2019 ◽  
Vol 2 (1) ◽  
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Physical Models ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ion Acoustic

Modified extended mapping method is further modified to discover traveling wave solutions of non- linear complex physical models, arising in various fields of applied sciences. The method is applied to three-dimensional ZakharovKuznetsov-Burgers equation in magnetized dusty plasma. Consequently different kinds of families of exact traveling wave solutions that represent electric field potential, electric and magnetic fields are fruitfully surveyed, with the help of Mathematica. The obtained novel exact traveling wave solutions are in different forms such as bright and dark solitary wave, periodic solitary wave, dark and bright soliton, etc., that are represented in the forms of trigonometric, hyperbolic, exponential and rational functions. The properties of some of the novel traveling wave solutions are shown by figures. The obtained results exhibit the effectiveness, power and exactness of the method that can be used for many other nonlinear problems.

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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