Phase transition from soliton to breather, soliton-breather molecules, breather molecules of the Caudrey-Dodd-Gibbon equation

Abstract

In this study, the Caudrey-Dodd-Gibbon equation is under investigation. The explicit first- to fourth-order solutions are represented using the distinctive auxiliary function involved in the bilinear form. These solutions allow us to discover several novel features of the equation: the transition from soliton to breather; soliton-breather molecules; breather molecules. Furthermore, during the interactions between these molecules, solitons and breathers in the molecules exchange their amplitudes and reach an entangled state with the same amplitude.