Non-Lie Symmetries and Supersymmetries

Abstract

Appeared more than one century ago, the classical Lie approach serves as a powerful toolin investigations of symmetries of partial differential equations. In the last three decadesthere appear essential generalizations of this approach. They are the modern version ofthe Lie-B¨acklund symmetries [1], the non-Lie approach [2–4], the conditional symmetryapproach [5–7], etc.I will speak about non-Lie symmetries of equations of mathematical physics. The term”non-Lie symmetries” has appeared in papers of Fushchych [2], the main ideas and basicresults of the non-Lie approach are outlined in our books [3, 4].To formulate the general idea of non-Lie symmetries, we consider a linear differentialequationL