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Toward a unification of the various techniques used to integrate nonlinear partial differential equations: Bäcklund and Darboux transformations vs. dressing method. (English) Zbl 0621.35095
After a historical survey on integrable nonlinear 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.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35G20 Nonlinear higher-order PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C05 Solutions to PDEs in closed form
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