Abstract

Based on Darboux transformation, we generate breather solutions sitting on zero background via module resonance for complex modified KdV equation. Then, some novel soliton molecules, breather molecules and breather-soliton molecules are obtained theoretically by module resonance and velocity resonance. Further, we study the higher-order breather-positons with zero background on the basis of degenerate Darboux transformation and module resonance for the first time. We discuss the dynamics of higher-order breather-positons in detail and propose related propositions. Finally, we find new elastic interactions between smooth positons and breather-positons by means of degenerate Darboux transformation and partial module resonance.

中文翻译：

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复杂的修正KdV方程的零背景上的新型孤子分子和呼吸正子

摘要

基于Darboux变换，我们通过模块共振针对复杂的修改的KdV方程生成零背景下的通气解。然后，通过模块共振和速度共振理论上获得了一些新颖的孤子分子，通气分子和通气孤子分子。此外，我们首次基于简并的Darboux变换和模块共振研究了背景为零的高阶呼吸正子。我们详细讨论了高阶呼吸正位的动力学，并提出了相关的命题。最后，我们通过简并的Darboux变换和部分模块共振发现了光滑的正电子与呼吸正电子之间的新的弹性相互作用。