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Journal of Statistical Physics

, Volume 160, Issue 5, pp 1432–1448 | Cite as

A Complexity Approach to the Soliton Resolution Conjecture

  • Claudio BonannoEmail author
Article

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.

Keywords

Solitons Complexity Entropy Dispersive PDEs 

Notes

Acknowledgments

I thank the referees for the comments and the suggestions that have greatly improved the paper. I am partially supported by “Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)” of Istituto Nazionale di Alta Matematica (INdAM), Italy.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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