A Nekhoroshev Type Theorem of Higher Dimensional Nonlinear Schrodinger Equations

作者：Zhou, Shidi; Geng, Jiansheng^*

来源：Taiwanese Journal of Mathematics, 2017, 21(5): 1115-1132.

DOI：10.11650/tjm/7951

• KAM theory
• Hamiltonian systems
• Schrodinger equation
• Birkhoff normal form

In this paper, we prove a Nekhoroshev type theorem for high dimensional NLS (nonlinear Schrodinger equations):
i partial derivative(t)u - Delta u + V * u + partial derivative((u) over bar)g(x, u, (u) over bar) = 0, x is an element of T-d, t is an element of R
where real-valued function V is sufficiently smooth and g is an analytic function. We prove that, for any given M is an element of N, there exists an epsilon(0) > 0, such that for any solution u = u(t, x) with initial data u(0) = u(0)(x) whose Sobolev norm parallel to u(0)parallel to(s) = epsilon < epsilon(0), during the time vertical bar t vertical bar <= epsilon(-M), its Sobolev norm parallel to u(t)parallel to(s) remains bounded by C-s epsilon.

• 出版日期2017-10
• 单位南京大学