Integrability Aspects and Soliton Solutions for a System Describing Ultrashort Pulse Propagation in an Inhomogeneous Multi-Component Medium

摘要

For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium,a system of coupled equations is analytically studied in this paper.Painleve analysis shows that this system admitsthe Painleve property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure,the Laxpair of this system is derived,and the Darboux transformation (DT) is constructed with the help of the obtainedLax pair.With symbolic computation,the soliton solutions are obtained by virtue of the DT algorithm.Figures areplotted to illustrate the dynamical features of the soliton solutions.Characteristics of the solitons propagating in aninhomogeneous multi-component nonlinear medium are discussed:(ⅰ) Propagation of one soliton and two-peak soliton;(ⅱ) Elastic interactions of the parabolic two solitons;(ⅲ) Overlap phenomenon between two solitons;(ⅳ) Collision oftwo head-on solitons and two head-on two-peak solitons;(ⅴ) Two different types of interactions of the three solitons;(ⅵ) Decomposition phenomenon of one soliton into two solitons.The results might be useful in the study on theultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media.