Geodesic
Attractors of nonlinear Hamiltonian partial differential equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 1, pp. 1-87

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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.
Keywords: Hamiltonian equations, nonlinear partial differential equations, wave equation, Maxwell equations, limiting amplitude principle, limiting absorption principle, attractor, steady states, stationary orbits, adiabatic effective dynamics, symmetry group, Schrödinger equation, wave-particle duality.
Mots-clés : Klein–Gordon equation, soliton, Lie group, quantum transitions 
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A. I. Komech; E. A. Kopylova. Attractors of nonlinear Hamiltonian partial differential equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 1, pp. 1-87. http://geodesic.mathdoc.fr/item/RM_2020_75_1_a0/