Dynamic Bifurcation Of The Fourth-order Schr(?)dinger Equation

This paper considers the fourth order Schr(?)dinger equation with Dirichlet bound-ary condition and periodic boundary condition respectively. When the parameter λ throughs the first critical value λ=αλ1, it proves that an attractor is bifurcated. The analysis is based on the basis of the recently created new attractor bifurcation theory, using eigenvalue analysis and the center manifold reduction method at the same time.The first chapter mainly introduces the background of nonlinear Schr(?)dinger equation, the basic theory of infinite dimensional dynamical system and method innovation.In the second chapter, we investigate the dynamic bifurcation of the fourth-order Schr(?)dinger equation with Dirichlet boundary condition.In the third chapter, we study the dynamic bifurcation of the fourth-order Schr(?)dinger equation with periodic boundary condition.