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arXiv · 2512.15487

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

Mats Ehrnström·Mark D. Groves
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Abstract

The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric `fully localised' 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 fullly localised 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.

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Mats Ehrnström, Mark D. Groves. 2025-12-17. A plethora of fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. https://arxiv.org/abs/2512.15487

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