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The Use of Factors to Discover Potential Systems or Linearizations

In: Geometric and Algebraic Structures in Differential Equations

Author

Listed:
  • George Bluman

    (University of British Columbia, Department of Mathematics)

  • Patrick Doran-Wu

    (University of British Columbia, Department of Mathematics)

Abstract

Factors of a given system of PDEs are solutions of an adjoint system of PDEs related to the system’s Fréchet derivative. In this paper, we introduce the notion of potential conservation laws, arising from specific types of factors, which lead to useful potential systems. Point symmetries of a potential system could yield nonlocal symmetries of the given system and its linearization by a noninvertible mapping. We also introduce the notion of linearizing factors to determine necessary conditions for the existence of a linearization of a given system of PDEs.

Suggested Citation

  • George Bluman & Patrick Doran-Wu, 1995. "The Use of Factors to Discover Potential Systems or Linearizations," Springer Books, in: P. H. M. Kersten & I. S. Krasil’Shchik (ed.), Geometric and Algebraic Structures in Differential Equations, pages 21-43, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0179-7_3
    DOI: 10.1007/978-94-009-0179-7_3
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