New interaction solutions in Mel’nikov equation obtained by modulating the phase shift

doi:10.1088/1674-1056/adaccb

中国物理B ›› 2025, Vol. 34 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/adaccb

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New interaction solutions in Mel’nikov equation obtained by modulating the phase shift

Mi Chen(陈觅)¹ and Zhen Wang(王振)^2,†

1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2 School of Mathematical Sciences, Beihang University, Beijing 100191, China

收稿日期:2024-10-29 修回日期:2025-01-03 接受日期:2025-01-22 出版日期:2025-04-15 发布日期:2025-04-15
通讯作者: Zhen Wang E-mail:wangzmath@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 52171251 and U21062251) and Program of Science and Technology Innovation of Dalian (Grant No. 2022JJ12GX036).

New interaction solutions in Mel’nikov equation obtained by modulating the phase shift

Mi Chen(陈觅)¹ and Zhen Wang(王振)^2,†

1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2 School of Mathematical Sciences, Beihang University, Beijing 100191, China

Received:2024-10-29 Revised:2025-01-03 Accepted:2025-01-22 Online:2025-04-15 Published:2025-04-15
Contact: Zhen Wang E-mail:wangzmath@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 52171251 and U21062251) and Program of Science and Technology Innovation of Dalian (Grant No. 2022JJ12GX036).

摘要/Abstract

摘要： The degradation and nonlinear interactions of a two-breather solution of the Mel'nikov equation are analyzed. By modulating the phase shift and limit method, we prove that in different regions near the non-singular boundaries, there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution. They are the interaction solution between soliton and breather, the two-soliton solution, and the two-breather solution with small amplitude, which all exhibit repulsive interactions; and the two-breather solution with small amplitude, which exhibits attractive interaction. Interestingly, a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.

关键词: Mel'nikov equation, breather solution, phase shift

Abstract: The degradation and nonlinear interactions of a two-breather solution of the Mel'nikov equation are analyzed. By modulating the phase shift and limit method, we prove that in different regions near the non-singular boundaries, there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution. They are the interaction solution between soliton and breather, the two-soliton solution, and the two-breather solution with small amplitude, which all exhibit repulsive interactions; and the two-breather solution with small amplitude, which exhibits attractive interaction. Interestingly, a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.

Key words: Mel'nikov equation, breather solution, phase shift

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons) 02.30.Jr (Partial differential equations)

Mi Chen(陈觅) and Zhen Wang(王振). New interaction solutions in Mel’nikov equation obtained by modulating the phase shift[J]. 中国物理B, 2025, 34(4): 40201-040201.

Mi Chen(陈觅) and Zhen Wang(王振). New interaction solutions in Mel’nikov equation obtained by modulating the phase shift[J]. Chin. Phys. B, 2025, 34(4): 40201-040201.

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New interaction solutions in Mel’nikov equation obtained by modulating the phase shift

New interaction solutions in Mel’nikov equation obtained by modulating the phase shift

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