The stability of full dimensional KAM tori for nonlinear Schrödinger equation

DOI10.1016/j.jde.2017.12.013zbMath1382.37079arXiv1705.01658OpenAlexW2963139009MaRDI QIDQ683484

Hongzi Cong, Yunfeng Shi, Jian-Jun Liu, Xiao Ping Yuan

Publication date: 6 February 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.01658

zbMATH Keywords

almost periodic solutionNLS equationfull-dimensional toriHamilton PDE

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (15)

About linearization of infinite-dimensional Hamiltonian systems ⋮ Long time stability of plane wave solutions to Schrödinger equation on Torus ⋮ Almost periodic invariant tori for the NLS on the circle ⋮ The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation ⋮ An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS ⋮ Stability and recursive solutions in Hamiltonian PDEs ⋮ The existence of almost-periodic solutions for 1-dimensional nonlinear Schrödinger equation with quasi-periodic forcing ⋮ On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range ⋮ Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ Analytic solutions of nonlinear elliptic equations on rectangular tori ⋮ On the stability of periodic multi-solitons of the KdV equation ⋮ ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION ⋮ Almost-periodic response solutions for a forced quasi-linear Airy equation ⋮ PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION

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