d-维环面上分数阶薛定谔方程解的长时间稳定性

The Long Time Stability for the Fractional Schrödinger Equations on d-Dimensional Torus

利用无穷维KAM理论及Birkhoff标准型技巧证明了一类d-维分数阶薛定谔方程解的全局存在性结果,即给出了解的长时间稳定性。该结果为研究由分数阶薛定谔方程定义的无穷维哈密顿动力系统的动力学行为提供了很好的依据。

The global existence of solutions for a class of d-dimensional fractional Schrödinger equations is proved by using infinite dimensional KAM theory and Birkhoff normal form technique.That is,the long-time stability of the solutions is given.The results provide a good basis for studying the dynamic behavior of infinite dimensional Hamiltonian Dynamical System defined by fractional Schrödinger equation.