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Русская версия

**Gerd Baumann**

Department of Mathematical Physics

University of Ulm, Albert-Einstein-Alle 11

D-89069 Ulm, Germany

**Joerg Volkmann**

Department of Mathematical Physics

University of Ulm, Albert-Einstein-Alle 11

D-89069 Ulm, Germany

In this article we discuss two methods of solving systems of partial differential equations. First we describe the Painleve test. In a second step a similarity analysis is carried out to motivate optimal systems. We present procedures of solving partial differential equations, which connect both methods. The connection between the methods is examplified by the KdV equation. Special points are the applications of the theorem of Strampp and the calculation of nonclassical symmetries via the algorithm of Clarkson.