Soliton molecules and novel smooth positons for the complex modified KdV equation

Abstract

In this research, based on Darboux transformation, a molecule consisting of two identical soliton waves is firstly obtained by velocity resonance for modified KdV equation. And we also get molecules containing a plurality of solitons. Further, we study the elastic interaction between soliton molecules and typical smooth higher-order positon via semi-degenerate Darboux transformation. Last but not least, we find a new type of smooth positons called rational positons. The dynamic properties of higher-order rational positon are discussed in detail and related propositions are given in this paper. The nature of rational positons is fundamentally different from that of typical smooth positons and breather positons. The method used in this paper to get interaction solutions and rational positons can be applied to other integrable equations as well.