Toward a unification of the various techniques used to integrate non-linear partial differential equations: Bäcklund and Darboux transformations vs. dressing method

Abstract

After a historical survey on integrable non-linear partial differential equations, we briefly review three methods often used to obtain their exact solutions, i.e. the Bäcklund transformation, the Darboux transformation and the dressing method introduced by Zakharov and Shabat in 1979. Then we elucidate their interrelations.