Quasi-periodic solutions of fractional nonlinear Schrödinger equation systems

Abstract

In this paper, the fractional nonlinear Schrödinger equation system with periodic boundary conditions is considered. I establish an abstract infinite-dimensional KAM theorem and apply it to fractional nonlinear Schrödinger equation system with real Fourier multiplier. By establishing a block diagonal normal form, we prove the existence of a class of Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite-dimensional invariant tori of an associated infinite-dimensional dynamic system.

COMMUNICATED BY:

• G. M. N'Guerekata

Keywords:

• Hamiltonian system
• fractional Schrödinger equation system
• Töplitz–Lipschitz property
• quasi-periodic solution

MSC:

• 37K55
• 74K43

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China (NSFC) [grant number 11801492], [grant number 61877052], [grant number 11871146] and Natural Science Foundation of Jiangsu Province (NSFJS) [grant number BK 20170472].