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.

EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2010 ◽  
Vol 24 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL ◽  
LUWAI WAZZAN
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Higher Dimensional

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh–coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

scholarly journals Solitons for the modified $(2 + 1)$-dimensional Konopelchenko–Dubrovsky equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiumei Lyu ◽  
Wei Gu
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
High Order ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Equation Approach ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Triangular Function

Abstract In the paper, we consider the modified $(2 + 1)$ ( 2 + 1 ) -dimensional Konopelchenko–Dubrovsky equations which possess high order nonlinear terms. Under the aid of Maple, we derive the exact traveling wave solutions of the mKDs by the auxiliary equation approach. Under some special conditions, Jacobi elliptic function solutions, degenerated triangular function solutions, and solitons for the mKD equations are constructed.

scholarly journals Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Zeid I. A. Al-Muhiameed ◽  
Emad A.-B. Abdel-Salam
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Jacobi Elliptic Function ◽  
Nonlinear Schrödinger ◽  
Function Solution ◽  
Balance Principle ◽  
Wave Solutions

With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.

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.

scholarly journals Stability Analysis and Assortment of Exact Traveling Wave Solutions for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2021 ◽  
pp. 2393-2400
Author(s):  
Mizal H. Alobaidi ◽  
Wafaa M. Taha ◽  
Ali H. Hazza ◽  
Pelumi E. Oguntunde
Keyword(s):  
Stability Analysis ◽  
Traveling Wave ◽  
Physical Meaning ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Exact Results ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
The Stability

     In this research, the Boiti–Leon–Pempinelli (BLP) system was used to understand the physical meaning of exact and solitary traveling wave solutions. To establish modern exact results, considered. In addition, the results obtained were compared with those obtained by using other existing methods, such as the standard hyperbolic tanh function method, and the stability analysis for the results was discussed.

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