具无界扰动的4阶非线性薛定谔方程的不变环面

Invariant Tori for the Forth Order Nonlinear Schrodinger Equation with Unbounded Perturbation

考虑了狄利克雷边条件下的四阶非线性薛定谔方程iu_t+u_(xxxx)+|u_x|~2u_(xx)=0.利用一个无穷维KAM定理,证明上述方程存在大量的n-不变环面,从而得到方程存在大量的时间拟周期解.

In this paper,we are concerned with the forth order nonlinear Schr?dinger(NLS)equation iut+uxxxx+|ux|2uxx=0,subject to Dirichlet boundary conditions.Using an infinite dimensional KAM theorem,we prove that there exist many n-dimensional invariant tori and thus many time quasi-periodic solutions for the above equation.