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arXiv · 1902.04643

Statistical Equilibrium of the Korteweg-de Vries and Benjamin-Ono Unidirectional Soliton Models

Brett Altschul
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Abstract

The Korteweg-de Vries and Benjamin-Ono nonlinear wave equations can describe solitary waves, all of which propagate in the same direction and which emerge from collisions with their shapes unchanged. There are technical challenges to giving a description of the thermal equilibrium of a dilute gas of such solitons. These challenges can be overcome by considering a stochastic source of new solitons located at $x=0$. The total intensity and the momentum distributions of the solitons emitted by such sources determine the equilibrium distribution of soliton momenta for $x>0$.

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Brett Altschul. 2019-10-30. Statistical Equilibrium of the Korteweg-de Vries and Benjamin-Ono Unidirectional Soliton Models. https://doi.org/10.1088/1742-5468%2Fab4982

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