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Book Review
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Book Information
Author(s):
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:
- 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), 91-106. MR 793075
- 3.
- L. V. Ovsiannikov, Group analysis of differential equations, Academic Press, New York, 1982. 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.
- P. J. Olver, Application of Lie groups to differential equations, Mathematical Institute, Oxford, June, 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
Additional Information:
Reviewer(s):
George W.
Bluman
Review Information:
Journal:
Bull. Amer. Math. Soc.
18
(1988),
73-78.
DOI:
10.1090/S0273-0979-1988-15606-6
PII:
S 0273-0979(1988)15606-6
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