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.
CITATION STYLE
Bonanno, C. (2015). A Complexity Approach to the Soliton Resolution Conjecture. Journal of Statistical Physics, 160(5), 1432–1448. https://doi.org/10.1007/s10955-015-1297-7
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