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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Author: Peter J. Olver
Title: Applications of Lie groups to differential equations
Additional book information: Graduate Texts in Mathematics, Volume 107, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, xxvi + 497 pp., $54.00. ISBN 0-387-96250-6.

References [Enhancements On Off] (What's this?)

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  • 2. F. Schwarz, Automatically determining symmetries of partial differential equations, Computing 34 (1985), no. 2, 91–106 (English, with German summary). MR 793075,
  • 3. L. V. Ovsiannikov, Group analysis of differential equations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. Translated from the Russian by Y. Chapovsky; Translation edited by William F. Ames. MR 668703
  • 4. G. W. Bluman and J. D. Cole, Similarity methods for differential equations, Springer-Verlag, New York, Berlin, 1974. MR 460846
  • 5. G. Birkhoff, Hydrodynamics-A study in logic, fact and similitude, 1st ed., Princeton Univ. Press, Princeton, 1950. MR 38180
  • 6. W. Miller, Jr., Symmetry and separation of variables, Addison-Wesley, Reading, Mass., 1971. MR 460751
  • 7. E. Noether, Invariante Variationsprobleme, Nachr. König. Gessell. Wissen. Göttingen, Math. -Phys. K1. (1918), 235-257.
  • 8. R. L. Anderson, S. Kumei, and C. E. Wulfman, Generalizations of the concept of invariance of differential equations. Results of applications to some Schrödinger equations, Phys. Rev. Lett. 28 (1972), 988-991. MR 398309
  • 9. P. J. Olver, Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215. MR 521611
  • 10. Peter J. Olver, Applications of Lie groups to differential equations, Lecture Notes, Oxford University, Mathematical Institute, Oxford, 1980. MR 673378
  • 11. V. I. Arnol'd, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier Grenoble 16 (1966), 319-361. MR 202082
  • 12. V. I. Arnol'd, The Hamiltonian nature of the Euler equations in the dynamics of a rigid body and an ideal fluid, Uspekhi Mat. Nauk 24 (1969), 225-226 (Russian). MR 277163
  • 13. C. S. Gardner, Korteweg-de Vries equation and generalizations. IV, The Korteweg-de Vries equation as a Hamiltonian system, J. Math. Phys. 12 (1971), 1548-1551. MR 286402

Review Information:

Reviewer: George W. Bluman
Journal: Bull. Amer. Math. Soc. 18 (1988), 73-78
American Mathematical Society