The Excitation Of Nonlinear Localized Waves In A Coupled Femtosecond Pulses System With Four Wave Mixing

Four wave mixing is an important nonlinear effect in the area of nonlinear optics,which induces the energy conversion between light beams.The influence of four wave mixing on ultrashort pulses has been studied preliminarily.However when the widths of ultrashort pulses were compressed further,namely for femtosecond pulses,the influence of four wave mixing on these femtosecond pulses has not been studied.Thus we study the propagation of optical pulses in a coupled femtosecond pulses system with four wave mixing and look forward to find abundant nonlinear localized waves and their special evolution dynamics in this system.In this thesis,firstly we give integrable generalized coupled Hirota equations with four wave mixing terms to describe the propagation of optical pulses in a coupled femtosecond pulses system with four wave mixing.Secondly,we use Darboux transformation and linear superposition method to find analytic solutions of these equations and we notice that these solutions contain abundant nonlinear localized waves.Next,by using these solutions,we study the transformation between different types of solitons(w-shaped soliton,anti-dark soliton,etc.)or soliton trains on plane wave backgrounds and oscillating solitons,breather-like nonlinear localized waves on periodic wave backgrounds.The relationship between nonlinear localized waves on plane wave backgrounds and on periodic wave backgrounds is discovered.Finally,calculating the perturbation energy of breather-like nonlinear localized waves as an example,we reveal that the energy conversion induced by four wave mixing is the reason lead to the appearance of these fresh nonlinear localized waves and special evolution dynamics.These results would enrich our knowledge of nonlinear localized waves in the coupled femtosecond pulses system with four wave mixing and help people to find nonlinear localized waves in these system experimentally.