Solitons, rogon-solitons and their propagations and reflections in three-component coupled nonlinear Schrödinger equation

Abstract

Soliton solution composed of e-exponential functions is generally a stable solitary wave, rational solution formed by a fraction of independent variables sometimes shows instantaneity, and rogon-soliton solution mentioned in this paper refers to the coupling of rational solution in a soliton solution. This work reports the fact that not only soliton solutions but also rogon-soliton solutions can be obtained for the three-component coupled nonlinear Schrödinger (TCCNLS) equation. Specifically, a new and more general TCCNLS equation with four constant parameters and its two Lax pairs are given, and then based on N-fold Darboux transformation (DT), the first-, second- and third-steps of the generalized DT (gDT) for a special case of the general TCCNLS equation are established. Some soliton solutions and rogon-soliton solutions with single and double spectral parameter(s) of the TCCNLS equation are obtained by empolying the established three stepts of the gDT. It is shown that the spectral parameter(s) contained in the obtained solutions has/have regular influences on both the propagations and reflections of solitons and rogon-solitons localized in the TCCNLS equation.