Darboux transformation, generalized Darboux transformation and vector breather solutions for a coupled variable-coefficient cubic-quintic nonlinear Schrödinger system in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Abstract

Non-Kerr media, twin-core nonlinear optical fibers and waveguides are widely applied in optical fiber communications. In order to model the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide, a coupled variable-coefficient cubic-quintic nonlinear Schrödinger system is investigated in this paper. For the two components of the electromagnetic fields, on the basis of the existing Lax pair, we take a gauge transformation to convert a Lax pair into an Ablowitz-Kaup-Newell-Segur system. Then we acquire a system, which is equal to the original system. The N-fold Darboux transformation is derived based on our Lax pair, where N is a positive integer. Applying Taylor series, we derive the N-fold generalized Darboux transformation. The second- and third-order vector breather solutions are obtained via the generalized Darboux transformation method. All our results depend on the variable coefficients of the original system. Our results might be of some use in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide system.