Nonlocally Related PDE Systems

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


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.


Potential Variable Nonlinear Wave Equation Extended Tree Potential System Lagrange System 
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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  • George W. Bluman
    • 1
    Email author
  • 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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