Attractors of Hamiltonian nonlinear partial differential equations
Abstract
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamics of solitons and their asymptotic stability. Results of numerical simulations are also given. Based on these results, we propose a new general hypothesis on attractors of -invariant nonlinear Hamiltonian partial differential equations. The obtained results suggest a novel dynamical interpretation of basic quantum phenomena: Bohr's transitions between quantum stationary states, wave-particle duality, and probabilistic interpretation.
Keywords
Cite
@article{arxiv.2212.14152,
title = {Attractors of Hamiltonian nonlinear partial differential equations},
author = {Andrew Comech and Alexander Komech and Elena Kopylova},
journal= {arXiv preprint arXiv:2212.14152},
year = {2023}
}
Comments
42 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1907.06998