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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

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?)

  • 1. S. Lie, Über die Integration durch bestimmte Integrale von einer Klasse linear partieller Differentialgleichungen, Arch. Math. 6 (1881), 328-368; also Gesammelte Abhandlungen, vol. III, B. G. Teubner, Leipzig and H. Aschehoug & Co., Kristiania, 1922 (Johnson Reprint Corporation, New York, London, 1973), 492-523.
  • 2. F. Schwarz, Automatically determining symmetries of partial differential equations, Computing 34 (1985), no. 2, 91–106 (English, with German summary). MR 793075 (87j:58103a), http://dx.doi.org/10.1007/BF02259838
  • 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 (83m:58082)
  • 4. G. W. Bluman and J. D. Cole, Similarity methods for differential equations, Springer-Verlag, New York-Heidelberg, 1974. Applied Mathematical Sciences, Vol. 13. MR 0460846 (57 #838)
  • 5. Garrett Birkhoff, Hydrodynamics. A Study in Logic, Fact, and Similitude, Princeton University Press, Princeton, N. J., 1950. MR 0038180 (12,365m)
  • 6. Willard Miller Jr., Symmetry and separation of variables, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. With a foreword by Richard Askey; Encyclopedia of Mathematics and its Applications, Vol. 4. MR 0460751 (57 #744)
  • 7. E. Noether, Invariante Variationsprobleme, Nachr. König. Gessell. Wissen. Göttingen, Math. -Phys. K1. (1918), 235-257.
  • 8. Robert Leonard Anderson, Sukeyuki Kumei, and Carl E. Wulfman, Generalization of the concept of invariance of differential equations. Results of applications to some Schrödinger equations, Phys. Rev. Lett. 28 (1972), no. 15, 988–991. MR 0398309 (53 #2162)
  • 9. Peter J. Olver, Evolution equations possessing infinitely many symmetries, J. Mathematical Phys. 18 (1977), no. 6, 1212–1215. MR 0521611 (58 #25341)
  • 10. Peter J. Olver, Applications of Lie groups to differential equations, Lecture Notes, Oxford University, Mathematical Institute, Oxford, 1980. MR 673378 (84k:58197)
  • 11. V. Arnold, 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), no. fasc. 1, 319–361 (French). MR 0202082 (34 #1956)
  • 12. V. I. Arnol′d, The Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid, Uspehi Mat. Nauk 24 (1969), no. 3 (147), 225–226 (Russian). MR 0277163 (43 #2900)
  • 13. Clifford S. Gardner, Korteweg-de Vries equation and generalizations. IV. The Korteweg-de Vries equation as a Hamiltonian system, J. Mathematical Phys. 12 (1971), 1548–1551. MR 0286402 (44 #3615)


Review Information

Reviewer: George W. Bluman
Journal: Bull. Amer. Math. Soc. 18 (1988), 73-78
DOI: http://dx.doi.org/10.1090/S0273-0979-1988-15606-6
PII: S 0273-0979(1988)15606-6



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