Two-dimensional stationary soliton gas

TL;DR

This paper develops a kinetic theory for two-dimensional stationary soliton gases within the KPII equation framework, analytically describing interactions like refraction and interference, and verifies predictions through numerical simulations.

Contribution

It introduces a novel kinetic equation for 2D soliton gases based on recent (1+1)D results and generalised hydrodynamics, extending soliton gas theory to two dimensions.

Findings

Analytical description of soliton gas refraction and interference.

Verification of theoretical predictions via large N-soliton numerical simulations.

Explicit evaluation of long-distance correlations in 2D soliton interactions.

Abstract

We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This (2+0)D reduction enables the construction of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalised hydrodynamics of the Boussinesq equation. We then use the kinetic theory to analytically describe two basic types of 2D soliton gas interactions: (i) refraction of a line soliton by a stationary soliton gas, and (ii) oblique interference of two soliton gases. We verify the analytical predictions by numerically implementing the corresponding KPII soliton gases via exact N-soliton solutions with N-large and appropriately chosen random distributions for the soliton parameters. We also explicitly evaluate the long-distance correlations for the two-component interference configurations. The results can be applied to a variety of physical systems, from shallow water waves to Bose-Einstein condensates.