Study On The Solitons In The Sasa-Satsuma Equation With The Continuous Wave Background

As an integrable case of the higher-order nonlinear Schr?dinger model,the Sasa-Satsuma(SS)equation can describe the nonlinear propagation of ultrashort pulses in a monomode fiber with the third-order dispersion,self-steepening,and stimulated Raman scattering effects.In this thesis,via the Darboux transformation we systematically construct the rational,mixed and exponential soliton solutions for the Sasa-Satsuma equation in the modulation stable region,and analyze the dynamical evolution properties of the soliton solutions.For three different types of soliton solutions with different degenerate conditions,we discuss the single solitons including the rational Mexican-hat(MH)solitons,and the exponential anti-dark and MH solitons.All of them can propagate stably at a constant velocity,in which the renormalization energy of the rational MH soliton is zero but that of the exponential one is not zero.Also,we analyze the asymptotic behavior of three types of soliton solutions under generic cases.As a result,we find the annihilation and creation of the rational MH soliton pair,the non-resonant interactions among one rational MH soliton and two mixed solitons,as well as the resonant interactions among three exponential solitons,where the first two kinds of soliton interactions are discovered for the first time.It is worth noting that the asymptotic analysis technique is developed in the asymptotic analysis of the rational and mixed soliton solutions,so that we derive the asymptotic solitons with the curved center trajectories,whose propagation speeds vary with time and space.Those new soliton interaction phenomena obtained in this thesis may have potential applications in all-optical digital computation and signal processing,and the improved asymptotic analysis may be applicable to the asymptotic analysis of soliton solutions of other integrable models.