Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

doi:10.1088/1674-1056/acb0c1

中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/acb0c1

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Zhonglong Zhao(赵忠龙)^1,†, Lingchao He(和玲超)², and Abdul-Majid Wazwaz³

1 School of Mathematics, North University of China, Taiyuan 030051, China;
2 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;
3 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

收稿日期:2022-11-28 修回日期:2022-12-30 接受日期:2023-01-06 出版日期:2023-03-10 发布日期:2023-04-04
通讯作者: Zhonglong Zhao E-mail:zhaozlhit@163.com,zhaozl@nuc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12101572) and the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-105).

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Zhonglong Zhao(赵忠龙)^1,†, Lingchao He(和玲超)², and Abdul-Majid Wazwaz³

1 School of Mathematics, North University of China, Taiyuan 030051, China;
2 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;
3 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

Received:2022-11-28 Revised:2022-12-30 Accepted:2023-01-06 Online:2023-03-10 Published:2023-04-04
Contact: Zhonglong Zhao E-mail:zhaozlhit@163.com,zhaozl@nuc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12101572) and the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-105).

摘要/Abstract

摘要： A large member of lump chain solutions of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation are constructed by means of the τ-function in the form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed, and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

关键词: lump chains, interaction solutions, BKP equation

Abstract: A large member of lump chain solutions of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation are constructed by means of the τ-function in the form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed, and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

Key words: lump chains, interaction solutions, BKP equation

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations) 02.30.Ik (Integrable systems)

Zhonglong Zhao(赵忠龙), Lingchao He(和玲超), and Abdul-Majid Wazwaz. Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves[J]. 中国物理B, 2023, 32(4): 40501-040501.

Zhonglong Zhao(赵忠龙), Lingchao He(和玲超), and Abdul-Majid Wazwaz. Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves[J]. Chin. Phys. B, 2023, 32(4): 40501-040501.

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Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

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