%0 Journal Article
%T Similarity Reductions and New Exact Solutions for B-Family Equations
%J American Journal of Mathematics and Statistics
%@ 2162-8475
%D 2012
%I 
%R 10.5923/j.ajms.20120203.05
%X In this paper, Lie-Group method is applied to the b-family equations which includes two important nonlinear partial differential equations Camassa--Holm (CH) equation and the Degasperis--Procesi (DP) equation. The complete Lie algebra of infinitesimal symmetries is established. Three nonequivalent sub-algebras of the complete Lie algebra are used to investigate similarity solutions and similarity reductions in the form of nonlinear ordinary equations (ODEs) for the b-family equations. The generalized He's Exp-Function method is used to drive exact solutions for the reduced nonlinear ODEs, some figures are given to show the properties of the solutions.
%K Similarity Reductions
%K Lie-Group Method
%K Exact Solution
%U http://article.sapub.org/10.5923.j.ajms.20120203.05.html