A complexity approach to the soliton resolution conjecture
Mathematical Physics
2015-09-02 v1 Analysis of PDEs
Dynamical Systems
math.MP
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.
Cite
@article{arxiv.1407.7570,
title = {A complexity approach to the soliton resolution conjecture},
author = {Claudio Bonanno},
journal= {arXiv preprint arXiv:1407.7570},
year = {2015}
}
Comments
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