On Separation of Variables for Integrable Equations of Soliton Type

Abstract

We propose a general scheme for separation of variables in the integrable Hamilto- nian systems on orbits of the loop algebra sl(2;C)£P(¸; ¸¡1). In particular, we illus- trate the scheme by application to modi¯ed Korteweg|de Vries (MKdV), sin(sinh)- Gordon, nonlinear SchrÄodinger, and Heisenberg magnetic equations.