Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

doi:10.1088/1674-1056/acb2c2

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50205-050205.doi: 10.1088/1674-1056/acb2c2

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Fuzhong Pang(庞福忠), Hasi Gegen(葛根哈斯)^†, and Xuemei Zhao(赵雪梅)

School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China

收稿日期:2022-10-17 修回日期:2022-12-26 接受日期:2023-01-13 出版日期:2023-04-21 发布日期:2023-04-28
通讯作者: Hasi Gegen E-mail:gegen@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 11965014).

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Fuzhong Pang(庞福忠), Hasi Gegen(葛根哈斯)^†, and Xuemei Zhao(赵雪梅)

School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China

Received:2022-10-17 Revised:2022-12-26 Accepted:2023-01-13 Online:2023-04-21 Published:2023-04-28
Contact: Hasi Gegen E-mail:gegen@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 11965014).

摘要/Abstract

摘要： The (2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semi-discrete Kadomtsev-Petviashvili I equation. This paper focuses on investigating the resonant interactions between two breathers, a breather/lump and line solitons as well as lump molecules for the (2+1)-dimensional elliptic Toda equation. Based on the N-soliton solution, we obtain the hybrid solutions consisting of line solitons, breathers and lumps. Through the asymptotic analysis of these hybrid solutions, we derive the phase shifts of the breather, lump and line solitons before and after the interaction between a breather/lump and line solitons. By making the phase shifts infinite, we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons. Through the asymptotic analysis of these resonant solutions, we demonstrate that the resonant interactions exhibit the fusion, fission, time-localized breather and rogue lump phenomena. Utilizing the velocity resonance method, we obtain lump-soliton, lump-breather, lump-soliton-breather and lump-breather-breather molecules. The above works have not been reported in the (2+1)-dimensional discrete nonlinear wave equations.

关键词: (2+1)-dimensional elliptic Toda equation, resonant interaction, lump molecules

Abstract: The (2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semi-discrete Kadomtsev-Petviashvili I equation. This paper focuses on investigating the resonant interactions between two breathers, a breather/lump and line solitons as well as lump molecules for the (2+1)-dimensional elliptic Toda equation. Based on the N-soliton solution, we obtain the hybrid solutions consisting of line solitons, breathers and lumps. Through the asymptotic analysis of these hybrid solutions, we derive the phase shifts of the breather, lump and line solitons before and after the interaction between a breather/lump and line solitons. By making the phase shifts infinite, we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons. Through the asymptotic analysis of these resonant solutions, we demonstrate that the resonant interactions exhibit the fusion, fission, time-localized breather and rogue lump phenomena. Utilizing the velocity resonance method, we obtain lump-soliton, lump-breather, lump-soliton-breather and lump-breather-breather molecules. The above works have not been reported in the (2+1)-dimensional discrete nonlinear wave equations.

Key words: (2+1)-dimensional elliptic Toda equation, resonant interaction, lump molecules

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons) 52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)) 04.30.Nk (Wave propagation and interactions)

Fuzhong Pang(庞福忠), Hasi Gegen(葛根哈斯), and Xuemei Zhao(赵雪梅). Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation[J]. 中国物理B, 2023, 32(5): 50205-050205.

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Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

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