Kinetic equations for a two-dimensional soliton gas

Gino Biondini; Thibault Bonnemain; Benjamin Doyon; Gennady El; Giacomo Roberti

Kinetic equations for a two-dimensional soliton gas

Pattern Formation and Solitons 2026-06-29 v1

Authors: Gino Biondini , Thibault Bonnemain , Benjamin Doyon , Gennady El , Giacomo Roberti

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.

Cite

@article{arxiv.2606.30582,
  title  = {Kinetic equations for a two-dimensional soliton gas},
  author = {Gino Biondini and Thibault Bonnemain and Benjamin Doyon and Gennady El and Giacomo Roberti},
  journal= {arXiv preprint arXiv:2606.30582},
  year   = {2026}
}