Reducibility of 1-d Schrödinger equation with unbounded time quasiperiodic perturbations. III

DOI10.1063/1.5048726zbMath1404.81089arXiv1807.06328OpenAlexW2884581606MaRDI QIDQ4644650

Riccardo Montalto, Dario Bambusi

Publication date: 8 January 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.06328

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbation theories for operators and differential equations in quantum theory (81Q15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Cites Work

• Unnamed Item
• KAM for autonomous quasi-linear perturbations of mKdV
• Quasi-periodic solutions for quasi-linear generalized KdV equations
• Quasi-periodic water waves
• Quasi-periodic solutions of forced Kirchhoff equation
• On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms
• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. II
• Nearly integrable infinite-dimensional Hamiltonian systems
• Reducibility of first order linear operators on tori via Moser's theorem
• Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with polynomial time-dependent perturbation
• Floquet Hamiltonians with pure point spectrum
• Time quasi-periodic gravity water waves in finite depth
• Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
• Standing waves on an infinitely deep perfect fluid under gravity
• Spectrum for quantum duffing oscillator and small-divisor equation with large-variable coefficient
• Proprietes asymptotiques du spectre dioperateurs pseuwdifferentiels sur IRⁿ
• Proprietes spectrales d'operators pseduo-differentiels
• WEAKLY REGULAR FLOQUET HAMILTONIANS WITH PURE POINT SPECTRUM
• On the growth of Sobolev norms for a class of linear Schrödinger equations on the torus with superlinear dispersion
• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. I
• A Reducibility Result for a Class of Linear Wave Equations on ${\mathbb T}^d$
• Time quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods
• Nash-Moser theory for standing water waves.