A complexity approach to the soliton resolution conjecture

Abstract

The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of solitons plus a radiative term. In this paper we use the complexity of a finite object, a notion introduced in Algorithmic Information Theory, to show that the soliton resolution conjecture is equivalent to the analogous of the second law of thermodynamics for the complexity of a solution of a dispersive equation.

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References in corpus (2)

• A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential
• Complexity for extended dynamical systems

Cited by in corpus (2)

• Solutions with compact time spectrum to nonlinear Klein--Gordon and Schroedinger equations and the Titchmarsh theorem for partial convolution
• Non-stiff methods for Airy flow and the modified Korteweg-de Vries equation