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An Involutive Reduction Method to Find Invariant Solutions for Partial Differential Equations

In: Computer Algebra in Scientific Computing CASC 2001

Author

Listed:
  • Joachim Engelmann

    (University of Ulm, Department of Mathematical Physics)

  • Gerd Baumann

    (University of Ulm, Department of Mathematical Physics
    Visual Analysis AG)

Abstract

A standard approach to solve partial diffrential equations is the construction of invariant solutions. These solutions have to fulfill an additional equation called the invariant surface condition. This condition represents the invariance of the equation under a symmetry transformation. To solve the coupled system of the differential equation and its invariant surface condition we used a Mathematica-package which combines involutive and heuristic methods to simplify and solve this coupled system. The procedure is presented by some examples.

Suggested Citation

  • Joachim Engelmann & Gerd Baumann, 2001. "An Involutive Reduction Method to Find Invariant Solutions for Partial Differential Equations," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC 2001, pages 177-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56666-0_14
    DOI: 10.1007/978-3-642-56666-0_14
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