New Exact Solutions for (3+1)-Dimensional Kadomtsev- Petviashvili Equation and Generalized (2+1)-Dimensional Boussinesq Equation

2005 ◽  
Vol 6 (2) ◽  
Author(s):  
Μ. F. El-Sabbagh ◽  
A. T. Ali
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equation ◽  
New Exact Solutions ◽  
Petviashvili Equation

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

Some New Exact Solutions of Jacobian Elliptic Function of Petviashvili Equation

2008 ◽  
Vol 49 (6) ◽  
pp. 1557-1560 ◽  
Author(s):  
Zhang Liang ◽  
Zhang Li-Feng ◽  
Li Chong-Yin ◽  
Wang Tie ◽  
Tan Yan-Ke
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Jacobian Elliptic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

An Improved Modified Extended tanh-Function Method

2006 ◽  
Vol 61 (3-4) ◽  
pp. 103-115 ◽  
Author(s):  
Zonghang Yang ◽  
Benny Y. C. Hon
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Boussinesq Equations ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variant Boussinesq Equations ◽  
Triangular Type

In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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