Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions

Abstract

We study solitary waves in the cylindrical Kadomtsev–Petviashvili equation designated to media with positive dispersion (the cKP1 equation). By means of the Darboux–Matveev transform, we derive exact solutions that describe two-dimensional solitary waves (lumps), lump chains, and their interactions. One of the obtained solutions describes the modulation instability of outgoing ring solitons and their disintegration onto a number of lumps. We also derive solutions describing decaying lumps and lump chains of a complex spatial structure—ripplons. Then, we study normal and anomalous (resonant) interactions of lump chains with each other and with ring solitons. Results obtained agree with the numerical data presented in Part I of this study [Hu et al., Chaos (2024)].