Construction Of Exact Solutions Of Three Nonlinear Schr(?)dinger-type Equations

Nonlinear partial differential equation is widely used in many fields such as quantum mechanics,epidemiology,plasma physics,fluid mechanics and ecological economic system.Therefore,it is of great practical significance to construct solutions of nonlinear partial differential equations.In this thesis,the modified(G'/G)-expansion method is used to study the(2+1)-dimensional Kundu-Mukherjee-Naskar equation and the fractionally modified unstable Schrodinger equation.And the dynamic system branch method is used to study and analyze the modified nonlinear Schrodinger equation with conformable fractional derivative.In chapter 2,by means of the modified(G'/G)-expansion method and the Riccati equation,a series of parametric exact traveling-wave solutions of the(2+1)-dimensional KunduMukherjee-Naskar equation are constructed.It includes trigonometric function solutions,hyperbolic function solutions and rational function solutions.At the same time,dark solitary wave solutions and periodic wave solutions are obtained when the parameters of the function are given special values.In chapter 3,a class of fractionally modified unstable Schrodinger equation is transformed into ordinary differential equation by fractional complex transformation.The modified(G'/G)-expansion method is employed to construct exact solutions of the fractionally modified unstable Schrodinger equation,and a series of exact solutions with parameters are obtained,including nine new solutions.In chapter 4,the nonlinear Schrodinger equation with integrated fractional correction is converted into ordinary differential equation by fractional complex transformation firstly.Then,the system equilibrium point,bifurcation phase diagram and evolution trajectory are obtained through the bifurcation theory of dynamical system.Finally,six types of exact solutions of the equation are constructed by integrating along different orbits.