Advertisement

Systematic Methods for Determining the Continuous Transformation Groups Admitted by Differential Equations

  • Carl E. Wulfman

Abstract

This talk will present some recent results obtained by using Lie’s systematic methods to uncover transformation groups admitted by several types of differential equations. We begin by sketching the methods.

Keywords

Determine Equation Schroedinger Equation Contact Transformation Infinitesimal Transformation Invariance Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    The variables zr take on hyperreal values as well, since zr + dzr is also a zr: c.f.e.g., K. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Academic Press, NY, 1976.Google Scholar
  2. 2.
    c.f. A. Cohen, An Introduction to the Lie Theory of One-parameter Groups, Stechert, NY, 1931, pp. 16–23.Google Scholar
  3. 3.
    For Lie-Backlund transformations of PDE’s with complex variables see S. Kumei, J. Math. Phys., 18, 256, (1977).CrossRefGoogle Scholar
  4. 4.
    N. Ibragimov, R. L. Anderson, J. Math. Anal. & Appl., 59, 145, (1977).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    S. Lie, Differentialgleichungen, Leipzig, 1891, reprinted, Chelsea, NY, 1967; pp. 299–305.Google Scholar
  6. 6.
    This seems to have first been recognized by Kumei (unpub. 1974).Google Scholar
  7. 7.
    For an example see T. Shibuya, C. Wulfman, Rev. Mex. Fis. 22, 171 (1973).MathSciNetGoogle Scholar
  8. 8.
    C. Wulfman, T. Sumi in Atomic Scattering Theory, J. Nuttall, ed., U. of Western Ontario, London, Ont., 1978; pp. 197202. See Also C. Wulfman, Dynamical Groups in Atomic and Molecular Physics, in Recent Advances in Group Theory and Their Application to Spectroscopy, J. Donini, ed., Plenum, NY, 1979.Google Scholar
  9. 9.
    c.f. J. L. Synge, Classical Physics, in Encyclopedia of Physics, S. Flugge, ed., Vol. III/1, Springer, Berlin, 1960.Google Scholar
  10. 10.
    R. L. Anderson, S. Kumei, C. Wulfman; a.) Phys. Rev. Lett., 28, 988, 1972; b.) Rev. Mex. Fix. 21, 1, (1972); c.) Rev. Mex. Fis. 21, 35, (1972); d.) J. Math. Phys. 14, 1527 (1973).MathSciNetADSGoogle Scholar
  11. 11.
    C. Wulfman, J. Phys. Al2, L73, (1979).Google Scholar
  12. 12.
    S. Kumei, a.) J. Math. Phys., 16, 2461, (1975); b.) ibid., 18, 256, (1977); c.) ibid. 19, 195, (1978).MathSciNetADSGoogle Scholar
  13. 13.
    N. H. Ibragimov, Lett. in Math. Phys. 1, 423, (1977).Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Carl E. Wulfman
    • 1
  1. 1.Department of PhysicsUniversity of the PacificStocktonUSA

Personalised recommendations