Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions
Zhao Zhang, Wen‐Cheng Hu, Qi Guo, Yury Stepanyants
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)].