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.

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 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.

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.

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.

scholarly journals Exact Solutions of the Kudryashov-Sinelshchikov Equation Using the MultipleG′/G-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yinghui He ◽  
Shaolin Li ◽  
Yao Long
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Rational Functions ◽  
Expansion Method ◽  
Jacobi Elliptic Functions ◽  
Hyperbolic Functions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

Exact traveling wave solutions of the Kudryashov-Sinelshchikov equation are studied by theG′/G-expansion method and its variants. The solutions obtained include the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric and rational functions. Many new exact traveling wave solutions can easily be derived from the general results under certain conditions. These methods are effective, simple, and many types of solutions can be obtained at the same time.

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