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Symmetry Operators and Solutions to Differential Equations in Algebra

  • Roei Nisim AsrafEmail author
Article
  • 45 Downloads

Abstract

The symmetry operator method for finding an analytical form for the solutions to a given PDE system is presented. The main tools for accomplishing this aim include computation and grading of the Lie algebra infinitesimals of symmetry groups admitted by a given PDE system, establishing fusion rules, and then checking the commutator relations after performing the grading. We discuss several examples of the differential systems of mathematical physics based on the splitting of heat and the Euler–Tricomi, generalized Cauchy–Riemann and Dirac equations in non-associative algebras.

Keywords

Symmetry algebra Algebra graduating Polynomial solutions 

Mathematics Subject Classification

58J70 76M60 

Notes

Acknowledgements

I thank Prof. Y. Krasnov for valuable suggestions, useful advice, and for encouraging me to write this paper, to Prof. J. Schiff for helpful comments and for suggesting Theorem 5.3, and Mrs. M. Beller who edited this paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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