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Non-classical Symmetries of Partial Differential Equations

In: Symmetry Analysis of Differential Equations with Mathematica®

Author

Listed:
  • Gerd Baumann

    (University of Ulm, Department of Mathematical Physics)

Abstract

The non-classical method of symmetry analysis is an extension of Lie’s classical method. This non-classical method was compiled by Bluman and Cole [1969] in connection with the analysis of the heat equation. This method allows us to derive another type of solutions which are different from solutions derived from Lie’s procedure. The method extends the classical approach to find solutions for linear and non-linear PDEs. This chapter contains the theoretical background of the method and demonstrates the application to different problems.

Suggested Citation

  • Gerd Baumann, 2000. "Non-classical Symmetries of Partial Differential Equations," Springer Books, in: Symmetry Analysis of Differential Equations with Mathematica®, chapter 6, pages 365-391, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2110-4_6
    DOI: 10.1007/978-1-4612-2110-4_6
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