Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation*

Abstract

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the (2+1)-dimensional fifth-order KdV system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the N-soliton solution, we obtain hybrid solutions consisting of soliton molecules, lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules, and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order KdV equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.