Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634769 | Applied Mathematics and Computation | 2007 | 9 Pages |
Abstract
For the nonlinear wave equation with damping term introduced in [Z.J. Yang, G.W. Chen, Initial value problem for a nonlinear wave equation with damping term, Acta Math. Appl Sin. 23 (2000) 45 (in Chinese)]utt-2buxxt+auxxxx=β(uxn)x,α>0,βâ 0,n⩾2,a new similarity reduction is presented by means of the direct reduction method due to Clark and Kruskal and the solutions for the equations with n⩾3 are given by using the new similarity reduction. By using similarity reductions and the ingenious construction of a proper auxiliary equation, some new special solutions such as one real solitary wave solution and one singular solitary wave solutions for β>0, and two complex solutions for β<0 are presented, respectively.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hongxia Wu, Tianyou Fan,