Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Hongcai Ma,Aiping Deng,Shupan Yue

doi:10.1007/s11071-022-07205-z

Abstract

Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada(gCDGKS) equation in fluid mechanics is given. By defining a novel restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the new proposed constraint, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves and breather solutions are found. Finally, with the support of long-wave limit method, the interaction between resonant Y-type solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived. These new results greatly extend the exact solution of (2+1)-dimensional gCDGKS equation already available in the literature and provide new ideas for studying the dynamical behaviors of fluid mechanic, soliton and shallow water wave and so on.

Highlights

As a local nonlinear wave, solitons have many interesting properties [1]
By adding some constraints on the N-soliton solution obtained by Hirota bilinear method, one can obtain many types of bound molecules
Through the velocity resonance mechanism, the soliton molecular solution first observed in physical experiments is obtained [2,3,4,5,6]

Summary

Introduction

As a local nonlinear wave, solitons have many interesting properties [1]. By adding some constraints on the N-soliton solution obtained by Hirota bilinear method, one can obtain many types of bound molecules. Chen and others constructed another constraint, which obtained the mixed solutions of resonant Y-type soliton and 1-order lump [22]. In order to obtain more interaction solutions between resonant Y-type solitons and other solutions, Li et al proposed a new constraint [24,25,26,27]. By this method, we can obtain the mixed solutions of resonant Y-shaped solitons and line waves, higher-order lumps, breather solutions and resonant Y-shaped solitons respectively.

N-soliton solution

Resonance Y-shape soliton

Interaction between resonant Y-shape soliton solution and lump solution

Conclusions

Data Availability Statements