Fermionic approach to soliton equations

In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the tau-function for charged free fermions in terms of determinants. Examples of how to get soliton, rational and dromion solutions from tau-functions for the various soliton equations are given. (C) 2011 Elsevier Inc. All rights reserved.