New explicit solutions of the nonlinear wave equations with damping term

作者：Wu Hongxia^*; Fan Tianyou

来源：Applied Mathematics and Computation, 2007, 191(2): 457-465.

DOI：10.1016/j.amc.2007.02.111

• wave equation with damping term
• similarity reductions
• real solitary wave solution
• complex solitary wave solution

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)]
u(tt) - 2bu(xxt) + au(xxxx) = beta(u(x)(n))(x), alpha > 0, beta > 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 beta > 0, and two complex solutions for beta < 0 are presented, respectively.

• 出版日期2007-8-15
• 单位北京理工大学