Solitary waves of the two-dimensional Benjamin equation

Abstract

In this paper, we study the existence of solitary waves associated to the two-dimensional Benjamin equation. This equation governs the evolution of waves at the interface of a two-fluid system in which surface-tension effects cannot be ignored. We classify the existence and nonexistence cases according to the sign of the transverse dispersion coefficients. Moreover, we show that the solitary waves of the 2D Benjamin equation, when they exist, converge to those of the KPI equation as the parameter preceding the nonlocal operator $H\partial^2_x$ goes to zero. We also prove the regularity of solitary waves, as well as their symmetry with respect to the transverse variable and their algebraic decay at infinity.