  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.
