2025/12/17 by Ehrnström, Mats, Groves, Mark D.
#35Q35 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2512.15487
The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number β>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.