International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1435-1448
doi:10.1155/IJMMS.2005.1435
Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation
Bao-Feng Feng1
, Takuji Kawahara2
, Taketomo Mitsui3
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
Abstract
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.