The Soliton Solutions Of Several Nonlinear Evolution Equations

In this paper,we investigate several nonlinear evolution equations including a general-ized coupled Hirota equation,a coupled Hirota equation and a generalized higher-order non-linear Schrodinger(NLS)equation.Based on the Darboux transformation(DT),we present the periodic solutions,breathers and rogue wave solutions of the generalized coupled Hirota euqation.For the coupled Hirota equation and the higher-order NLS equation,we construct the breather-to-soliton conversions and display the nonlinear waves interactions.The structure of the present paper is organized as follows:In chapter one,we review the development process of the soliton theory,and present the DT method and its development.Finally,the overall works and arrangements of this paper are summarized.In chapter two,a generalized coupled Hirota equation with higher-order and linear cou-pling terms is investigated.Based on the Lax integrable property,the DT algorithm has been constructed.Some new solutions under the vanishing and non-vanishing backgrounds are derived,including periodic solutions,breathers and rogue wave solutions.In chapter three,we study a coupled Hirota equation which can describe the pulse propagation in coupled optical waveguides.Via the DT method,we construct the breather-to-soliton conversions,derive several kinds of localized and periodic waves,and analyze the characteristics of the interactions among these nonlinear waves of this equation.In chapter four,we focus on a generalized NLS equation with two free parameters,includ-ing the third-order and fourth-order dispersion with matching higher-order nonlinear effects.The results show that the breather solution can be converted into some types of localized and periodic waves under specified parameter conditions.Coupled with rich graphical examples,the coexistence and interaction between different nonlinear structures are displayed.In chapter five,we summarize the conclusion in this paper and indicate the research emphasis in the future.