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2019•arXiv (Cornell University)Open access

A KAM Theorem for Higher Dimensional Reversible Nonlinear Schrödinger Equations

Yingnan Sun, Zhaowei Lou, Jiansheng Geng

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Abstract

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrödinger systems on $d-$torus $\mathbb{T}^d$.

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What this paper is about

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrödinger systems on $d-$torus $\mathbb{T}^d$.

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Available abstract

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrödinger systems on $d-$torus $\mathbb{T}^d$.

Key concepts: Kolmogorov–Arnold–Moser theorem, Torus, Hamiltonian system, Nonlinear system, Mathematics, Mathematical physics, Hamiltonian (control theory), Class (philosophy)

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