关键词: Coupled Schr¨odinger-Boussinesq equations, traveling wave transformation,
Riccati equations, solitary wave solution

Abstract:

A system comprised of the nonlinear Schr¨odinger equation coupled to the
Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled
non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed.
To examine its solitary wave solutions, a reduced set of ordinary differential equations are
considered by a simple traveling wave transformation. It is then shown that several new
solutions (either functional or parametrical) can be obtained systematically, in addition to
rederiving all known ones by means of our simple and direct algebra method with the help
of the computer algebra system Maple.

Key words: Coupled Schr¨odinger-Boussinesq equations, traveling wave transformation,
Riccati equations, solitary wave solution