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 bou...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52171251 and U21062251)Program of Science and Technology Innovation of Dalian(Grant No.2022JJ12GX036).
文摘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.
