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arXiv · 2606.30582

Kinetic equations for a two-dimensional soliton gas

Gino Biondini·Thibault Bonnemain·Benjamin Doyon·Gennady El·Giacomo Roberti
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Abstract

We formulate a general system of kinetic equations for a non-stationary two-dimensional gas of elastically interacting line solitons and apply it to the description of a soliton gas governed by the Kadomtsev-Petviashvili II (KPII) equation. We then verify the predictions of the kinetic theory in two analytically tractable problems: the oblique interaction of a KPII line soliton with a one-dimensional soliton condensate of the Korteweg-de Vries equation, and the interaction of a trial KPII soliton with a monochromatic KPII soliton gas. In both cases, we compare the analytical results with direct numerical simulations obtained by constructing two-dimensional soliton gases via exact KPII $N$-soliton solutions for large $N$, using appropriately chosen random distributions of soliton parameters. The comparison demonstrates excellent agreement, thereby providing strong validation of the proposed kinetic theory of 2D non-equilibrium soliton gases.

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Gino Biondini, Thibault Bonnemain, Benjamin Doyon, Gennady El, Giacomo Roberti. 2026-06-29. Kinetic equations for a two-dimensional soliton gas. https://arxiv.org/abs/2606.30582

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