On the inverse spectral problem for the quasi-periodic Schrödinger equation

DOI10.1007/s10240-013-0058-xzbMath1296.35168arXiv1209.4331OpenAlexW2963608868MaRDI QIDQ2249435

David Damanik, Michael Goldstein

Publication date: 1 July 2014

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4331

zbMATH Keywords

inverse spectral problemKAM theoremDiophantine conditionquasi-periodic Schrödinger equationresonances of arbitrary order

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

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Cites Work

• Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• KAM for the nonlinear Schrödinger equation
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Absolutely continuous spectrum for 1D quasiperiodic operators.
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• Integrals of nonlinear equations of evolution and solitary waves

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