Nonlocally Related PDE Systems

  • George W. Bluman
  • Alexei F. Cheviakov
  • Stephen C. Anco
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 168)

Abstract

Up to now, for a given PDE system, we have considered the calculation and application of its local symmetries (point, contact or higher-order) as well as the calculation of its local conservation laws. In particular, it has been shown how to use local symmetries to map solutions to other solutions; how to use local symmetries of given and target PDEs as an aid in relating them; how to use point or contact symmetries to determine whether a given PDE system can be mapped invertibly to some PDE system belonging to a target class of PDE systems that is completely characterized by its point symmetries as well as determine an explicit mapping when one exists; how to use multipliers yielding local conservation laws to determine whether a given nonlinear PDE system can be mapped invertibly to some linear PDE system as well as determine a specific mapping when one exists. Moreover, as it is well known, local symmetries can be used to find specific solutions (invariant solutions) of PDEs; this application is considered and extended in Chapter 5.

Keywords

Potential Variable Nonlinear Wave Equation Extended Tree Potential System Lagrange System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  • George W. Bluman
    • 1
  • Alexei F. Cheviakov
    • 2
  • Stephen C. Anco
    • 3
  1. 1.Department of MathematicsThe University of British ColumbiaVancouverCanada
  2. 2.Department of Mathematics and StatisticsUniversity of SaskatchewanSaskatoonCanada
  3. 3.Department of MathematicsBrock UniversitySt. CatharinesCanada

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