Darboux Transformation And Exact Solutions Of Coupled Gerdjikov-Ivanov Equation

Utilizing the classical Darboux transformation and the generalized Darboux transformation,this thesis mainly studies the coupled Gerdjikov–Ivanov(coupled GI)equation which is also called coupled derivative nonlinear Schr(?)dinger ?(coupled DNLS?)equation.We obtain some exact solutions under plane wave backgrounds,including solitons,breathers,rogue waves and the interaction between rogue waves and other types of nonlinear localized waves.In chapter 2,based on the symmetric relations of the Lax pair,2-fold Darboux transformation for the coupled GI equation is constructed.We obtain solitons,breathers,breather fission,soliton fusion and dark-bright rogue wave solutions.In addition,we show some figures by using Mathematica and analyse the dynamic behavior.In chapter 3,with the aid of limit technique and Taylor expansion,we construct the -fold generalized Darboux transformation of the coupled GI equation.We display the high-order fundamental rogue wave,the interaction between high-order rogue wave and multi-solitons or multi-breathers.