International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1435-1448

Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation

Bao-Feng Feng,1 Takuji Kawahara,2 Taketomo Mitsui,3 and Youn-Sha Chan4

1Department of Mathematics, The University of Texas – Pan American, Edinburg 78541-2999, TX, USA
2Department of Aeronautics and Astronautics, Kyoto University, Kyoto 606-8501, Japan
3Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan
4Department of Computer and Mathematical Sciences, University of Houston-Downtown, One Main Street, Houston 77002-1001, TX, USA

Received 23 November 2004

Copyright © 2005 Bao-Feng Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the solitary waves and their interaction for a six-order generalized Boussinesq equation (SGBE) both numerically and analytically. A shooting method with appropriate initial conditions, based on the phase plane analysis around the equilibrium point, is used to construct the solitary-wave solutions for this nonintegrable equation. A symmetric three-level implicit finite difference scheme with a free parameter θ is proposed to study the propagation and interactions of solitary waves. Numerical simulations show the propagation of a single solitary wave of SGBE, and two solitary waves pass by each other without changing their shapes in the head-on collisions.