On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials

By H. Eliasson, Sergei B. Kuksin. 2009

168 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4943c78bdb9e6301c8faa809e7364d820c5ffd2a

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

KAM for the nonlinear beam equation (2016, background): “The approach of [17, 16] is different from that of [8, 9] and allows to analyse the linear stability of the obtained KAM-solutions.”
An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds (2013, methodology): “Using KAM techniques, Eliasson-Kuksin [14, 15] proved existence and stability of quasi-periodic solutions for NLS with Fourier multipliers, see also Procesi-Xu [25].”
KAM for Reversible Derivative Wave Equations (2012, background): “This concept is clearly modelled on the Hamiltonian case in [3], [23], and it is related to the Töplitz-Lipschitz functions in Eliasson-Kuksin [13]-[12] (see also [14]), but there are differences.”
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential (2010, background): “Clearly an advantage of the KAM approach is to provide also a stability result: the linearized equations on the perturbed invariant tori are reducible to constant coefficients, see also [22].”
Quasi-periodic solutions with Sobolev regularity of NLS on $\mathbb {T}^d$ with a multiplicative potential (2013, background): “Clearly an advantage of the KAM approach is to provide also a stability result: the linearized equations on the perturbed invariant tori are reducible to constant coefficients, see also [22].”
KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation (2014, unknown): “This is achieved introducing the notion of “quasi-Töplitz” vector field, which is inspired to the concept of “quasi-Töplitz” and “Töplitz-Lipschitz” Hamiltonians, developed, respectively, in Procesi-Xu [39] and Eliasson-Kuksin [19], [20] (see also Geng-You-Xu [21], Grébert-Thomann [23], Procesi-Proc”