A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equations via the linear superposition principle

Abstract

In this paper, the existence and non-existence of resonant multi-soliton solutions to two different (2+1)-dimensional Hirota–Satsuma–Ito (HSI) equations are explored. After applying the linear superposition principle we generate resonant multi-soliton solutions to the first HSI equation which appeared in the theory of shallow water wave. The conditions of real resonant multi-soliton solutions are revealed. The presented resonant multi-soliton solutions exhibit the inelastic collision phenomenon among the involved solitary waves. Particularly, upon choosing appropriate parameters, we demonstrate the characteristics of inelastic interactions among the multi-front kink waves both graphically and theoretically. Moreover, non-existence of resonant multi-soliton solution is considered for the generalized HSI equation via the linear superposition principle.