> Details

Cheviakov, Alexei F.

An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics

Reference
management

Bookmarks

Remove from
bookmarks

Share this on Whatsapp

Close

Bookmarks



You can manage bookmarks using lists, please log in to your user account for this.
  • Media type: E-Article
  • Title: An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics
  • Contributor: Cheviakov, Alexei F.
  • Published: AIP Publishing, 2008
  • Published in: Journal of Mathematical Physics, 49 (2008) 8
  • Language: English
  • DOI: 10.1063/1.2956502
  • ISSN: 0022-2488; 1089-7658
  • Keywords: Mathematical Physics ; Statistical and Nonlinear Physics
  • Origination:
  • Footnote:
  • Description: Lie point symmetries and nonlocal symmetries of partial differential equation (PDE) systems are widely used for construction of exact invariant solutions. In this paper we describe an extended algorithmic procedure that, for a given nonlocal (potential) symmetry, can yield additional exact solutions, which cannot be found using the usual algorithm. In particular, such additional solutions are exact solutions of the given PDE system, but are not invariant solutions of the corresponding potential system. As an example, we consider a tree of nonlocally related PDE systems for Lagrange planar gas dynamics equations and classify its nonlocal symmetries for an ideal polytropic gas. For two different nonlocal symmetries of the Lagrange system, we demonstrate that the extended method yields wider classes of exact solutions than the usual method.