New exact solutions and conservation laws of the -dimensional dispersive long wave equations

2009 ◽  
Vol 373 (2) ◽  
pp. 214-220 ◽  
Author(s):  
Na Liu ◽  
Xiqiang Liu ◽  
Hailing Lü
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Wave Equations ◽  
New Exact Solutions ◽  
Long Wave

Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations

2009 ◽  
Vol 64 (9-10) ◽  
pp. 597-603 ◽  
Author(s):  
Zhong Zhou Dong ◽  
Yong Chen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Symmetry Group ◽  
Infinite Number ◽  
Wave Equations ◽  
Direct Method ◽  
Discrete Groups ◽  
Point Symmetry Group ◽  
Long Wave ◽  
Full Symmetry

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

New Exact Solutions to (2+1)-Dimensional Dispersive Long Wave Equations

2004 ◽  
Vol 42 (6) ◽  
pp. 811-813 ◽  
Author(s):  
Zhi Hong-Yan ◽  
Lü Zhuo-Sheng ◽  
Zhang Hong-Qing
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
New Exact Solutions ◽  
Long Wave

Exact solutions and conservation laws for coupled generalized Korteweg–de Vries and quintic regularized long wave equations

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1425-e1434 ◽  
Author(s):  
S. Hamdi ◽  
W.H. Enright ◽  
W. E Schiesser ◽  
J.J. Gottlieb
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Wave Equations ◽  
Long Wave ◽  
De Vries

The Exp-function Method for the Riccati Equation and Exact Solutions of Dispersive Long Wave Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 663-670 ◽  
Author(s):  
Sheng Zhang ◽  
Wei Wang ◽  
Jing-Lin Tong
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
New Exact Solutions ◽  
Long Wave

In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method is more powerful. It is shown that the Exp-function method provides a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics.

scholarly journals New exact solutions of coupled generalized regularized long wave equations

2017 ◽  
Vol 25 (4) ◽  
pp. 400-405 ◽  
Author(s):  
K.R. Raslan ◽  
Talaat S. EL-Danaf ◽  
Khalid K. Ali
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
New Exact Solutions ◽  
Long Wave
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