Almost periodic solutions of one dimensional Schrödinger equation with the external parameters

DOI10.1007/S10884-013-9302-9zbMath1288.35431OpenAlexW2128297302WikidataQ115383549 ScholiaQ115383549MaRDI QIDQ2377298

Xindong Xu, Jiansheng Geng

Publication date: 28 June 2013

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

Full work available at URL: https://doi.org/10.1007/s10884-013-9302-9

zbMATH Keywords

Schrödinger equationKAM theoryalmost periodic solutionstrong Töplitz-Lipschitz propertyWhitney family

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to functional-differential equations (34K14) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (14)

Almost-periodic solutions for a quasi-periodically forced nonlinear Schrödinger equation ⋮ Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing ⋮ Almost periodic invariant tori for the NLS on the circle ⋮ The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation ⋮ Invariant tori of full dimension for second KdV equations with the external parameters ⋮ Stability and recursive solutions in Hamiltonian PDEs ⋮ Small amplitude weak almost periodic solutions for the 1d NLS ⋮ The existence of almost-periodic solutions for 1-dimensional nonlinear Schrödinger equation with quasi-periodic forcing ⋮ Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing ⋮ A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS ⋮ ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION ⋮ Almost-periodic response solutions for a forced quasi-linear Airy equation ⋮ Full dimension tori of Schrödinger equation ⋮ Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity (|u|^2pu)_x

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• Quasi-Töplitz Functions in KAM Theorem
• Newton's method and periodic solutions of nonlinear wave equations
• On the construction of almost periodic solutions for a nonlinear Schrödinger equation
• Almost periodic solutions for a class of higher-dimensional beam equations

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