Bound-state solitons for a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber

In this paper, we study a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber for two orthogonally polarized optical pulses. With respect to the slowly-varying envelopes of two interacting optical modes and based on the existing binary Darboux transformation, we obtain four types of the bound-state solitons: degenerate-I, degenerate-II, degenerate–non-degenerate, and non-degenerate–non-degenerate bound-state solitons. We graphically analyze the interactions between the degenerate or non-degenerate solitons and four types of the bound-state solitons. When the degenerate solitons interact with the bound-state solitons, amplitudes and widths of the degenerate solitons remain unchanged. When the non-degenerate solitons interact with the bound-state solitons, amplitudes and widths of the bound-state solitons remain unchanged.

Quasi-Grammian solutions of the generalized Heisenberg magnet model

In this paper we use standard binary Darboux transformation to obtain the quasi-Grammian multi-soliton solutions of generalized Heisenberg magnet model in two dimensions. We also discuss the model based on the Lie group SU(n) and obtain explicit solutions of the model for the SU(2) case.