Attractors of nonlinear Hamiltonian PDEs

2014/09/06 by Alexander Komech, Komech, Alexander · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1409.2009

40 pages, 9 figures

arxiv created 2015/11/28 · arxiv updated 2015/12/01

Abstract

This is a survey of results on long time behavior and attractors for nonlinear Hamiltonian partial differential equations, considering the global attraction to stationary states, stationary orbits, and solitons, the adiabatic effective dynamics of the solitons, and the asymptotic stability of the solitary manifolds. The corresponding numerical results and relations to quantum postulates are considered.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• Existence of solitary waves in higher dimensions
• Asymptotic dynamics of nonlinear Schrödinger equations: Resonance‐dominated and dispersion‐dominated solutions
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

Cited by

• Lectures on Quantum Mechanics for mathematicians
• Attractors of Hamilton nonlinear partial differential equations

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