Symbolic computation on soliton dynamics and Bäcklund transformation for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity

Abstract

In this paper, we study the generalized coupled nonlinear Schrödinger equations with the cubic-quintic nonlinearity and arbitrary coupling parameters which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Dark–dark N- and bright–dark two-soliton solutions are derived with symbolic computation. The bilinear Bäcklund transformation and the corresponding one-soliton solution are also given. Interactions of the dark–dark solitons including the repulsive and coherent interactions are investigated analytically and graphically, which are different from those in previous studies. The relationship between the amplitude and the velocity of the dark soliton is studied, especially the soliton with the small amplitude catches up with the one with the large amplitude. Head-on and overtaking interactions of dark–dark solitons are presented. Interactions between a stationary dark soliton and another dark one are shown. The asymptotic analysis shows that the interaction of dark–dark two solitons is elastic. The periodic attraction and repulsion of the bright–dark two solitons in the bound state are also analyzed, which are in accordance with those in the bright–dark vector soliton studies but different from the asymmetric and symmetric stationary bound states of Manakov bright–dark solitons.