arXiv subjects

Shidi Zhou

Publications and source records attributed to Shidi Zhou.

2 recordsLinked to original sources

arXiv2017

An abstract infinite dimensional KAM theorem with application to nonlinear higher dimensional Schrodinger equation systems

In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real Fourier Multiplier. By establishing a block-diagonal normal form, We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.

math.DS↗

arXiv2017

An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation

In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract infinite dimensional KAM theorem and apply it to the completely resonant beam equation. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional tori.

math.DS↗