Soliton molecules and asymmetric solitons in three fifth order systems via velocity resonance

Abstract

Abstract Soliton molecules can be formed in some possible mechanisms both theoretically and experimentally. In this paper, we introduce a new mechanism, namely the velocity resonant, to find soliton molecules. Under the velocity resonance mechanism, two solitons can form a kink-antikink molecule, an asymmetric soliton, a two-peak soliton and/or a far away bounded molecule depended on the selections of the wave numbers and the distance between two solitons of a molecule. The results are exhibited via three well known fifth order integrable systems which serve as a general fluid model, as well as models many other physical fields.