The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation

2019/05/21 by Hongzi Cong, Xiaoping Yuan, Cong, Hongzi +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1905.08398

openalex publication_date 2019/05/21 · openalex created_date 2019/05/29 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the existence and linear stability of full dimensional tori with subexponential decay for 1-dimensional nonlinear wave equation with external parameters, which relies on the method of KAM theory and the idea proposed by Bourgain \citeBJFA2005.

Citations

• Newton's method and periodic solutions of nonlinear wave equations
• On invariant tori of full dimension for 1D periodic NLS
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation
• The stability of full dimensional KAM tori for nonlinear Schrödinger equation

Cited by

• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
• Invariant sets through resonant normal form for infinite dimensional holomorphic vector fields
• On almost periodic solutions to NLS without external parameters

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• The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation