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

Zhao Zhang; Wencheng Hu; Qi Guo; Yury Stepanyants

doi:10.1063/5.0175716

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

Chaos. 2024 Jan 1;34(1):013132. doi: 10.1063/5.0175716.

Authors

Zhao Zhang¹, Wencheng Hu², Qi Guo¹, Yury Stepanyants^{3

4}

Affiliations

¹ Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, People's Republic of China.
² School of Physics and Optoelectronic Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China.
³ School of Mathematics, Physics and Computer Sciences, University of Southern Queensland, Toowoomba, QLD 4350, Australia.
⁴ Department of Applied Mathematics, Nizhny Novgorod State Technical University, n.a. R.E. Alekseev, 24 Minin St., Nizhny Novgorod 603950, Russia.

PMID: 38252780
DOI: 10.1063/5.0175716

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)].