Jacobian elliptic function expansion solutions for the Wick-type stochastic coupled KdV equations

2007 ◽  
Vol 32 (5) ◽  
pp. 1679-1685 ◽  
Author(s):  
Zheng-Yi Ma ◽  
Jia-Min Zhu
Keyword(s):  
Elliptic Function ◽  
Jacobian Elliptic Function ◽  
Kdv Equations ◽  
Function Expansion ◽  
Coupled Kdv Equations

Painlevé Properties And Exact Solutions Of The Generalized Coupled Kdv Equations

2005 ◽  
Vol 60 (5) ◽  
pp. 313-320 ◽  
Author(s):  
Li-Jun Ye ◽  
Ji Lin
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Jacobi Elliptic Function ◽  
Negative Index ◽  
Kp Hierarchy ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Function Expansion ◽  
Coupled Kdv Equations ◽  
Jacobi Elliptic Function Expansion

The generalized coupled Korteweg-de Vries (GCKdV) equations as one case of the four-reduction of the Kadomtsev-Petviashvili (KP) hierarchy are studied in details. The Painlevé properties of the model are proved by using the standard Weiss-Tabor-Carnevale (WTC) method, invariant, and perturbative Painlev´e approaches. The meaning of the negative index k = −2 is shown, which is indistinguishable from the index k = −1. Using the standard and nonstandard Painlevé truncation methods and the Jacobi elliptic function expansion approach, some types of new exact solutions are obtained.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

General Jacobian elliptic function expansion method and its applications

2004 ◽  
Vol 13 (6) ◽  
pp. 798-804 ◽  
Author(s):  
Zhu Jia-Min ◽  
Ma Zheng-Yi ◽  
Fang Jian-Ping ◽  
Zheng Chun-Long ◽  
Zhang Jie-Fang
Keyword(s):  
Elliptic Function ◽  
Expansion Method ◽  
Jacobian Elliptic Function ◽  
Function Expansion
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