Two-component generalized nonlinear Schrödinger equations and their soliton and breather solutions

Abstract

In this paper, a cluster of two-component generalized nonlinear Schrödinger equations is generated in terms of zero-curvature equation and polynomial expansion of the spectral parameter, which can be used to illustrate effects on various nonlinear phenomena. After that, explicit representations of classical Darboux transformation and generalized perturbation (n,M)-fold Darboux transformation of the above equations are constructed. Localized wave solutions including soliton solutions, degenerate soliton solutions, soliton solutions interacting with degenerate soliton solutions, breather solutions and degenerate breather solutions are subsequently acquired via the classical Darboux matrix. Meanwhile, degenerate soliton solutions are acquired by the generalized perturbation (n,M)-fold Darboux transformation. Analyses of these solutions are shown through a series of figures ultimately.