Linear integral equations and multicomponent nonlinear integrable systems II

Abstract

In a previous paper (I) an extension of the direct linearization method was developed for obtaining solutions of multicomponent generalizations of integrable nonlinear partial differential equations (PDE's). The method is based on a general type of linear integral equations containing integrations over an arbitrary contour with an arbitrary measure in the complex plane of the spectral parameter. In I the general framework has been presented, with as immediate application the direct linearization of multicomponent versions of the nonlinear Schrödinger equation and the (complex) modified Korteweg-de Vries equation. In the present paper we treat a varìety of examples of other multicomponent PDE's, and we also discuss Miura transformations and gauge equivalences. The examples include the direct linearization of multicomponent generalizations of the isotropic Heisenberg spin chain equation, the complex sine-Gordon equation, the Getmanov equation, the derivative non-linear Schrödinger equation and the massive Thirring model equations.