四阶Schrodinger方程的动态分歧

Dynamic Bifurcation of the Four-Order Schrodinger Equation

对具有Dirichlet边界条件的四阶Schrdinger方程给出了分歧分析,证明了当参数λ穿过第一临界值λ=αλ1时,该问题分歧出一个吸引子.该分析以最近创立的新的吸引子分歧理论为基础,同时运用了特征值分析和中心流形约化方法.

A bifurcation analysis on the four-order Schrodinger equation with Dirichlet boundary condition is presented in this paper.It is proved that the problem bifurcates an attractor asλcrosses the first critical valueλ=αλ1.The analysis is based on a newly developed attractor bifurcation theory,together with the eigenvalue analysis and the center manifold reduction.