Symmetry, full symmetry groups, and some exact solutions to a generalized Davey–Stewartson system

2008 ◽  
Vol 49 (10) ◽  
pp. 103503 ◽  
Author(s):  
Biao Li ◽  
Wang-Chuan Ye ◽  
Yong Chen
Keyword(s):  
Exact Solutions ◽  
Symmetry Groups ◽  
Full Symmetry

scholarly journals Full Symmetry Groups and Exact Solutions to BKP and GKP Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Bo Ren ◽  
Jian-Yong Wang
Keyword(s):  
Exact Solutions ◽  
Symmetry Group ◽  
Symmetry Groups ◽  
Point Groups ◽  
Full Symmetry ◽  
The Relationship

We investigate the (2+1)-dimensional nonlinear BKP and GKP equations with the modified direct CK’s method. Then, we get its Lie point groups and the full symmetry group, and a relationship is constructed between the new solutions and the old one. Based on the relationship, the new solutions can be obtained by using a given solution of the equations.

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.

B-determining equations: applications to nonlinear partial differential equations

1995 ◽  
Vol 6 (3) ◽  
pp. 265-286 ◽  
Author(s):  
O. V. Kaptsov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Physical Importance

We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

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