scholarly journals All exact traveling wave solutions of the combined KdV-mKdV equation

2014 ◽  
Vol 2014 (1) ◽  
pp. 261 ◽  
Author(s):  
Yong Huang ◽  
Yonghong Wu ◽  
Fanning Meng ◽  
Wenjun Yuan
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

scholarly journals White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended G ′ / G -Expansion Method

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhao Li ◽  
Peng Li ◽  
Tianyong Han
Keyword(s):  
White Noise ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Hermite Transform ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
White Noise Functional

In this paper, white noise functional solutions of Wick-type stochastic fractional mixed KdV-mKdV equations have been obtained by using the extended G ′ / G -expansion method and the Hermite transform. Firstly, the Hermite transform is used to transform Wick-type stochastic fractional mixed KdV-mKdV equations into deterministic fractional mixed KdV-mKdV equations. Secondly, the exact traveling wave solutions of deterministic fractional mixed KdV-mKdV equations are constructed by applying the extended G ′ / G -expansion method. Finally, a series of white noise functional solutions are obtained by the inverse Hermite transform.

scholarly journals An Extended Auxiliary Function Method and Its Application in mKdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yafeng Xiao ◽  
Haili Xue ◽  
Hongqing Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Auxiliary Function ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

An extended auxiliary function method is presented for constructing exact traveling wave solutions to nonlinear partial differential equations. The main idea of this method is to take full advantage of the solutions to the elliptic equation to construct exact traveling wave solutions for nonlinear partial differential equations. mKdV equation is chosen to illustrate the application of the extended auxiliary function method. Consequently, more new exact traveling wave solutions are derived that are not obtained by the previously known methods.

More Exact Traveling Wave Solutions for Compound KdV Equation and MKdV Equation

2012 ◽  
Vol 433-440 ◽  
pp. 3642-3648
Author(s):  
Dong Bo Cao ◽  
Liu Xian Pan ◽  
Jia Ren Yan
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Trigonometric Function ◽  
Transform Method ◽  
Elimination Method ◽  
Matlab Software ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

Compound KdV equation and MKdV equation are investigated in the presented work, with the aid of Matlab software, using the trigonometric function transform method and the Wu elimination method, and more exact traveling wave solutions are obtained for compound KdV equation and MKdV equation.

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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