Soliton Solutions of Integrable Hierarchies and Coulomb Plasmas

TL;DR

This paper uncovers connections between soliton solutions of integrable hierarchies and the thermodynamics of Coulomb plasmas, revealing how certain solitons model plasma systems at specific conditions.

Contribution

It demonstrates how soliton solutions of KP and BKP hierarchies correspond to Coulomb plasma states and applies soliton theory methods to statistical mechanics of these systems.

Findings

Soliton solutions describe 2D plasmas at fixed temperature and boundary conditions.

Reductions of hierarchies model 1D and 2D plasma systems.

Methods of soliton theory are applied to plasma statistical mechanics.

Abstract

Some direct relations between soliton solutions of integrable hierarchies and thermodynamical quantities of the Coulomb plasmas on the plane are revealed. We find that certain soliton solutions of the Kadomtsev-Petviashvili (KP) and B-type KP (BKP) hierarchies describe two-dimensional one or two component plasmas at special boundary conditions and fixed temperatures. It is shown that different reductions of integrable hierarchies describe one (two) component plasmas or dipole gases on one-dimensional submanifolds embedded in the two-dimensional space. We demonstrate application of the methods of soliton theory to statistical mechanics of such systems.