Determinant solutions and asymptotic state analysis for an integrable model of transient stimulated Raman scattering

Abstract In this paper, the transient stimulated Raman scattering equations, which describe the stimulated Raman scattering in the transient limit, are investigated by Darboux transformation. Considering the trivial initial solutions, the explicit N-soliton solutions in determinant form for the transient stimulated Raman scattering equations are presented. Based on the explicit solutions formula, the one- and two-soliton solutions are given explicitly. The asymptotic state analysis of the two-soliton solutions is conducted. And different soliton propagation phenomena are discussed and illustrated including but not limited to the flat-top soliton, the two-hump soliton and bound two soliton with periodic structure, which is good for understanding the interaction properties under different wave parameters.