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
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.
Fund: 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).
Corresponding Authors:
Zhen Wang
E-mail: wangzmath@163.com
Cite this article:
Mi Chen(陈觅) and Zhen Wang(王振) New interaction solutions in Mel’nikov equation obtained by modulating the phase shift 2025 Chin. Phys. B 34 040201
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