Stability of 2D solitons for a sixth order Boussinesq type model

We study orbital stability of the solitary wave of least energy for a nonlinear 2D Benney–Luke model of higher order related to long water waves with small amplitude in the presence of strong surface tension. We follow a variational approach which includes the characterization of the ground state solution set associated with solitary waves. We use the Hamiltonian structure of this model to establish the existence of an energy functional conserved in time for the modulated equation associated with this Benney–Luke type model. For wave speed near zero or one, and in the regime of strong surface tension, we prove the orbital stability result by following a variational approach.

Keywords

Cauchy problem, solitary waves, variational methods, orbital stability

2010 Mathematics Subject Classification

35B35, 35Q35, 76B25

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Published 13 May 2015