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Appendix: How to find the symmetry group of a differential equation

Part of the Lecture Notes in Mathematics book series (LNM,volume 762)

Keywords

  • Vector Field
  • Symmetry Group
  • Heat Equation
  • Local Group
  • Maximal Rank

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References

  1. Bluman, G. W. and Cole, J. D., "The General Similarity Solution of the Heat Equation," J. Math. Mech., (11) 18 (1969), pp. 1025–1042.

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  2. Bluman, G. W. and Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, Applied Math. Sci. No. 13, New York, 1974.

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  3. Eisenhart, L. P., Continuous Groups of Transformations, Princeton University Press, Princeton, N.J., 1933.

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  4. Olver, P. J., "Symmetry Groups and Group Invariant Solutions of Partial Differential Equations," to appear, J. Diff. Geom.

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  5. Ovsjannikov, L. V., Group Properties of Differential Equations, transl. by G. W. Bluman, 1967 (unpublished).

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  6. Palais, R. S., "A Global Formulation of the Lie Theory of Transformation Groups," Memoris of the A. M. S. No. 22, Providence, R. J., 1957.

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  7. Palais, R. S., ed., Seminar on the Atiyah-Singer Index Theorem, Annals of Math Studies, No. 57, Princeton University Press, Princeton, N. J., 1965. (Chapter 4).

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  8. Warner, F. W., Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman and Company, Glenview, Ill. 1971.

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© 1979 Springer-Verlag

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Olver, P.J. (1979). Appendix: How to find the symmetry group of a differential equation. In: Group Theoretic Methods in Bifurcation Theory. Lecture Notes in Mathematics, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087463

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  • DOI: https://doi.org/10.1007/BFb0087463

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09715-0

  • Online ISBN: 978-3-540-38487-8

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