Some semirational solutions and their interactions on the zero-intensity background for the coupled nonlinear Schrödinger equations

• Published in: Communications in nonlinear science & numerical simulation Vol. 67; pp. 403 - 413
• Main Authors: Jiang, Yan, Qu, Qi-Xing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2019; Elsevier Science Ltd
• Subjects: Amplitudes; Coupled nonlinear Schrödinger equations; Degenerate solitons; Generalized Darboux transformation; Mathematical analysis; Nonlinear equations; Schrodinger equation; Semirational solutions; Simulation; Solitary waves; Wave interaction; Semirational solutions; Degenerate solitons; Coupled nonlinear Schrödinger equations; Generalized Darboux transformation
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2018.07.023

•New semirational solutions for the coupled nonlinear Schr.dinger equations are obtained.•Those obtained solutions are called as the type-I and type-II degenerate soliton solutions.•The propagation of degenerate solitons on the zero-intensity background are discussed.•Some interactions and bound states on the zero-intensity background are investigated. In this paper, we present two types of the semirational solutions for the coupled nonlinear Schrödinger equations through employing the generalized Darboux transformation. Based on those semirational solutions, some nonlinear wave interactions on the zero-intensity background are investigated. For example, we find that (i) two degenerate solitons with the same amplitudes draw close to each other first, then interact and finally apart from each other, while in the general two-soliton interaction, two solitons with the same amplitudes will periodically attract and repel, and form a bound state, (ii) the elastic and inelastic interactions occur between one regular soliton and degenerate solitons, (iii) some novel bound states arise due to the existence of the degenerate solitons.