# Attractors of Hamilton nonlinear partial differential equations

## TL;DR

This paper surveys the theory of attractors in nonlinear Hamiltonian PDEs, discussing stability, solitons, and numerical results, and proposes a new conjecture linking these attractors to fundamental quantum phenomena.

## Contribution

It provides a comprehensive survey of attractor theory in Hamiltonian PDEs and introduces a novel conjecture connecting attractors to quantum mechanics interpretations.

## Key findings

- Results on global attraction to stationary states and solitons
- Numerical simulations illustrating attractor behavior
- A new conjecture linking attractors to quantum phenomena

## 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 simulation are given. The obtained results allow us to formulate 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's transitions between quantum stationary states, wave-particle duality and probabilistic interpretation.