On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications |
| |
Institution: | 1. Centre de Recherches Mathématiques, Université de Montréal, Succ. Centre-Ville, CP 6128, Montréal (QC) H3C 3J7, Canada;2. Department of Mathematics and Computer Science, Université du Québec à Trois-Rivières, CP 500, Trois-Rivières (QC) G9A 5H7, Canada;3. Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warszawa, Poland |
| |
Abstract: | This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are removed. As a consequence, new insights into other types of conditional symmetries arise. We then apply the so-called PDE Lie systems to the derivation and analysis of Lie algebras of conditional symmetries. In particular, we develop a method for obtaining solutions of a higher-order system of PDEs via the solutions and geometric properties of a PDE Lie system, whose form gives a Lie algebra of conditional symmetries of the Clairin type. Our methods are illustrated with physically relevant examples such as nonlinear wave equations, the Gauss–Codazzi equations for minimal soliton surfaces, and generalised Liouville equations. |
| |
Keywords: | Conditional symmetry PDE Lie system Jet bundle Clairin formalism Gauss–Codazzi equation Generalised Liouville equation |
本文献已被 ScienceDirect 等数据库收录! |
|