Pucci, Edvige; Saccomandi, Giuseppe Potential symmetries and solutions by reduction of partial differential equations. (English) Zbl 0789.35146 J. Phys. A, Math. Gen. 26, No. 3, 681-690 (1993). Summary: We determine some necessary conditions for a given partial differential equation \({\mathcal E}\), written in conservative form to admit a potential symmetry (PS). A PS of \({\mathcal E}\) is a point symmetry of the auxiliary system \({\mathcal S}_ p\) obtained introducing a potential as further unknown function, then a PS leads to the construction of solutions via the classical reduction method. Given a PS, we introduce an algorithm that allows us to determine a class of \({\mathcal E}\)-solutions which includes the ones obtained as invariant solutions under the related point symmetry of \({\mathcal S}_ p\). As examples, we consider a Fokker-Planck equation, a wave equation in non-homogeneous media and a quasilinear wave equation. Cited in 1 ReviewCited in 23 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 58J70 Invariance and symmetry properties for PDEs on manifolds 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:reduction method; Fokker-Planck equation; quasilinear wave equation PDFBibTeX XMLCite \textit{E. Pucci} and \textit{G. Saccomandi}, J. Phys. A, Math. Gen. 26, No. 3, 681--690 (1993; Zbl 0789.35146) Full Text: DOI