Existence and non existence of solitons for a 1D Benney-Luke model of higher order

Abstract

We shall establish the existence and non existence of solitons (travelling waves of finite energy) for a Benney-Luke equation of higher order, which includes models for long water waves with small amplitude. Following a variational approach, solitons are characterized as critical points of the action functional. Existence of solitons follows by the Concentration-Compactness principle by P.-L. Lions, applied to an appropriated minimization problem. It is also shown that solitons are smooth.