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We show the existence and the analyticity of solitons (solitary waves of finite energy) for a 2D-Boussinesq-Benney-Luke type system that emerges in the study of the evolution of long water waves with small amplitude in the presence of surface tension. We follow a variational approach by characterizing travelling waves as minimizers of some functional under a suitable constrain. Using Lion’s concentration-compactness principle, we prove that any minimizing sequences converges strongly, after an appropriate translation, to a minimizer. The Boussinesq-Benney-Luke system is formally close to the Benney-Luke equation and to the Kadomtsev-Petviashivili (KP) equation. For wave speed small and surface tension large, we assure some physical sense for this water wave system by establishing that a suitable (renormailized) family of solitons of the Boussinesq-Benney-Luke system converges to a nontrivial soliton for the KP-I equation.

Existence, physical sense and analyticity of solitons for a 2D Boussinesq-Benney-Luke system