Long time stability of KAM tori for the nonlinear Schr\"odinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
TL;DR
This paper proves the long-term stability of KAM tori in the nonlinear Schrödinger equation on multi-dimensional tori, advancing understanding of the equation's long-term dynamics.
Contribution
It establishes the long time stability of KAM tori for the nonlinear Schrödinger equation in arbitrary dimensions, a significant extension of previous results.
Findings
Proves long time stability of KAM tori
Applicable to nonlinear Schrödinger equations in any dimension
Enhances understanding of long-term behavior of solutions
Abstract
In this paper, we prove the long time stability of KAM tori for the nonlinear Schr\"odinger equation on the torus with arbitrary dimensions.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Advanced Mathematical Physics Problems