Exact traveling wave solutions for a generalized Hirota–Satsuma coupled KdV equation by Fan sub-equation method

2011 ◽  
Vol 375 (23) ◽  
pp. 2201-2210 ◽  
Author(s):  
Dahe Feng ◽  
Kezan Li
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Coupled Kdv Equation

EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED HIROTA–SATSUMA COUPLED KdV EQUATION

2010 ◽  
Vol 24 (22) ◽  
pp. 4333-4355 ◽  
Author(s):  
ZHU LI
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Function Method ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Jacobi Elliptic Function ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Coupled Kdv Equation ◽  
Jacobi Elliptic Function Method

Exact traveling wave solutions of the generalized Hirota–Satsuma coupled KdV equation are obtained by the generalized Jacobi elliptic function method.

scholarly journals Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 742 ◽  
Author(s):  
Tao Liu
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Singular Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Fifth Order ◽  
Fkdv Equation

We study a fifth order time-fractional KdV equation (FKdV) under meaning of the conformal fractional derivative. By trial equation method based on symmetry, we construct the abundant exact traveling wave solutions to the FKdV equation. These solutions show rich evolution patterns including solitons, rational singular solutions, periodic and double periodic solutions and so forth. In particular, under the concrete parameters, we give the representations of all these solutions.

scholarly journals On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

2017 ◽  
Vol 7 (3) ◽  
pp. 265-270
Author(s):  
Gülnur Yel ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Trigonometric Function ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this work, we construct the exact traveling wave solutions of the fractional (2+1)-dimensional Davey-Stewartson equation system (D-S) that is complex equation system using the Modified Trial Equation Method (MTEM). We obtained trigonometric function solutions by this method that are new in literature.

scholarly journals A Generalized KdV Equation of Neglecting the Highest-Order Infinitesimal Term and Its Exact Traveling Wave Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xianbin Wu ◽  
Weiguo Rui ◽  
Xiaochun Hong
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Dynamic Properties ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Wave Model ◽  
Dark Soliton ◽  
Exact Traveling Wave Solutions ◽  
Generalized Kdv Equation ◽  
Wave Solutions

We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop-soliton solutions, broken loop-soliton solutions, broken wave solutions of U-form and C-form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical softwareMaple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.

scholarly journals Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hossam A. Ghany ◽  
M. Zakarya
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Noise Analysis ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Variable Coefficients ◽  
Hermite Transform ◽  
Exact Traveling Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions

F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.

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.

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