Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

doi:10.1088/1674-1056/ada7da

中国物理B ›› 2025, Vol. 34 ›› Issue (4): 40202-040202.doi: 10.1088/1674-1056/ada7da

Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Xi-Yu Tan(谭茜宇) and Wei Tan(谭伟)†

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

收稿日期:2024-10-10 修回日期:2025-01-06 接受日期:2025-01-09 出版日期:2025-04-15 发布日期:2025-04-15
通讯作者: Wei Tan E-mail:tanwei1008@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12461047) and the Scientific Research Project of the Hunan Education Department (Grant No. 24B0478).

Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Xi-Yu Tan(谭茜宇) and Wei Tan(谭伟)†

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

Received:2024-10-10 Revised:2025-01-06 Accepted:2025-01-09 Online:2025-04-15 Published:2025-04-15
Contact: Wei Tan E-mail:tanwei1008@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12461047) and the Scientific Research Project of the Hunan Education Department (Grant No. 24B0478).

摘要/Abstract

摘要： Based on a new bilinear equation, we investigated some new dynamic behaviors of the (2+1)-dimensional shallow water wave model, such as hybridization behavior between different solitons, trajectory equations for lump collisions, and evolution behavior of multi-breathers. Firstly, the $N$-soliton solution of Ito equation is studied, and some high-order breather waves can be obtained from the $N$-soliton solutions through paired-complexification of parameters. Secondly, the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method, and the motion velocity and trajectory equations of high-order lump waves are analyzed. Moreover, based on the trajectory equations of the higher-order lump solutions, we give and prove the trajectory theorem of 1-lump before and after interaction with $n$-soliton. Finally, we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method. Meanwhile, some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.

关键词: Ito equation, trajectory equation, multi-solitons, dynamic behavior

Abstract: Based on a new bilinear equation, we investigated some new dynamic behaviors of the (2+1)-dimensional shallow water wave model, such as hybridization behavior between different solitons, trajectory equations for lump collisions, and evolution behavior of multi-breathers. Firstly, the $N$-soliton solution of Ito equation is studied, and some high-order breather waves can be obtained from the $N$-soliton solutions through paired-complexification of parameters. Secondly, the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method, and the motion velocity and trajectory equations of high-order lump waves are analyzed. Moreover, based on the trajectory equations of the higher-order lump solutions, we give and prove the trajectory theorem of 1-lump before and after interaction with $n$-soliton. Finally, we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method. Meanwhile, some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.

Key words: Ito equation, trajectory equation, multi-solitons, dynamic behavior

中图分类号: (Partial differential equations)

02.30.Jr

05.45.Yv (Solitons) 02.30.Ik (Integrable systems)

Xi-Yu Tan(谭茜宇) and Wei Tan(谭伟). Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model[J]. 中国物理B, 2025, 34(4): 40202-040202.

Xi-Yu Tan(谭茜宇) and Wei Tan(谭伟). Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model[J]. Chin. Phys. B, 2025, 34(4): 40202-040202.

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Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

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