Periodic solutions of some infinite-dimensional Hamiltonian systems associated with nonlinear partial difference equations. I

DOI10.1007/BF01229204zbMath0696.35185OpenAlexW4236520459MaRDI QIDQ910618

Claudio Albanese, Jürg Fröhlich

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf01229204

zbMATH Keywords

eigenfunctionsrandom coefficientsrandom potentialnonlinear Schrödinger equationsnonlinear eigenvaluesnonlinear wave equationsbifurcation techniques

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Partial functional-differential equations (35R10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (12)

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with nonlinear partial difference equations. II ⋮ Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory ⋮ Multifractals competing with solitons on Fibonacci optical lattices ⋮ On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential ⋮ Quasi-periodic solutions of nonlinear random Schrödinger equations ⋮ Anderson localization for time quasi-periodic random Schrödinger and wave equations ⋮ BREATHERS IN INHOMOGENEOUS NONLINEAR LATTICES: AN ANALYSIS VIA CENTER MANIFOLD REDUCTION ⋮ Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions ⋮ Schrödinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist ⋮ Long time Anderson localization for the nonlinear random Schrödinger equation ⋮ Anomalous thermostat and intraband discrete breathers ⋮ Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems

Cites Work

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• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Constructive proof of localization in the Anderson tight binding model
• Anderson localization for multi-dimensional systems at large disorder or large energy
• Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium
• Localization in disordered, nonlinear dynamical systems
• Localised solutions of Hartree equations for narrow-band crystals
• A continuation method for nonlinear eigenvalue problems
• A pure point spectrum of the stochastic one-dimensional Schrödinger operator

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