The Existence of Full Dimensional KAM tori for Nonlinear Schrödinger equation

2021/03/27 by Cong, Hongzi · 3 citations
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2103.14777

Abstract

In this paper, we will prove the existence of full dimensional tori for 1-dimensional nonlinear Schrödinger equation with periodic boundary conditions iu_t-u_xx+V*u+ε|u|⁴u=0,\hspace12ptx∈\mathbbT, where V* is the convolution potential. Here the radius of the invariant torus satisfies a slower decay, i.e. I_n∼ e^{- lnσ|n|}, as |n|→∞, for any σ>2, which improves the result given by Bourgain (J. Funct. Anal. 229 (2005), no.1, 62-94).

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• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
• On almost periodic solutions to NLS without external parameters
• The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation

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