The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation
Hongzi Cong, Siming Li, Xiaoqing Wu
TL;DR
This paper proves the existence and stability of full-dimensional KAM tori for the one-dimensional nonlinear Klein-Gordon equation, demonstrating almost-periodic solutions in the non-relativistic limit with subexponential decay.
Contribution
It extends KAM theory to establish full-dimensional tori for the nonlinear Klein-Gordon equation under periodic boundary conditions, using Bourgain's method.
Findings
Existence of full-dimensional KAM tori
Linear stability of these tori
Almost-periodic solutions with subexponential decay
Abstract
In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary conditions. Specifically, by employing the method introduced in \cite{Bourgain2005JFA}, we establish the existence and linear stability of full-dimensional tori with subexponential decay for the equation.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Photonic Systems · Nonlinear Differential Equations Analysis