A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equations via the linear superposition principle. (January 2020)

• Record Type: Journal Article
• Authors: Kuo, Chun-Ku; Ma, Wen-Xiu
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: Hirota–Satsuma–Ito equation -- Linear superposition principle -- Resonant multi-soliton solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111592
• Languages: English
• ISSNs: 0362-546X

Abstract

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.