A plethora of fully localized solitary waves for the full-dispersion Kadomtsev–Petviashvili equation

Abstract The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta \gt 1/3$ , also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric ‘fully localized’ or ‘lump’ solitary waves which decay to zero in all spatial directions. The full-dispersion KP-I equation is obtained by retaining the exact dispersion relation in the modelling from the water-wave problem. In this paper, we show that the FDKP-I equation also has a family of symmetric fully localized solitary waves which are obtained by casting it as a perturbation of the KP-I equation and applying a suitable variant of the implicit-function theorem.