Attractors of nonlinear Hamiltonian partial differential equations

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Abstract

This is a survey of the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. Included are results on global attraction to stationary states, to solitons, and to stationary orbits, together with results on adiabatic effective dynamics of solitons and their asymptotic stability, and also results on numerical simulation. The results obtained are generalized in the formulation of a new general conjecture on attractors of $G$-invariant nonlinear Hamiltonian partial differential equations. This conjecture suggests a novel dynamical interpretation of basic quantum phenomena: Bohr transitions between quantum stationary states, de Broglie's wave-particle duality, and Born's probabilistic interpretation.Bibliography: 212 titles.

About the authors

Aleksandr Il'ich Komech

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)

Email: alexander.komech@univie.ac.at
Doctor of physico-mathematical sciences, Professor

Elena Andreevna Kopylova

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)

Email: elena.kopylova@univie.ac.at

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