Solitary-wave and multi-pulsed traveling-wave solutions of Boussinesq systems

Abstract

This paper studies traveling-wave solutions of the partial differential equations which model waves in a horizontal water channel traveling in both directions. The existence of solitary-wave solution on a number of systems is proved; the multi-pulsed traveling-wave solutions with any number of troughs are found numerically; the bifurcation diagrams of these solutions with respect to phase speed and with respect to system parameters are presented.