A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem

Abstract

We present a new form of Backlund transformations which gives a unified method of finding Backlund transformations for s9lutions of certain nonlinear evolution equations and constructing the inverse scattering problem for solving the initial-value problem. We consider the sine-Gordon equation, the modified. Korteweg-de Vries equation and the Korteweg-de Vries equatidn as examples.