Journal of Statistical Physics, Vol. 99, Nos. 34, 2000. p. 751-767.
Some direct relations are given between soliton solutions of integrable hierarchies and thermodynamic quantities of the Coulomb plasmas on the plane. We find that certain soliton solutions of the KadomtsevPetviashvili (KP) and B-type KP (BKP) hierarchies describe 2D one- or two-component lattice plasmas at special boundary conditions and fixed temperatures. It is shown that different reductions of integrable hierarchies describe pure or dipole
Coulomb gases on 1D submanifolds embedded in the 2D space.