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Zbl 0785.58003
Olver, Peter J.
Applications of Lie groups to differential equations. 2nd ed. (English)
[B] Graduate Texts in Mathematics. 107. New York: Springer-Verlag. xxviii, 513 p. DM 108.00; sfr 108.00 (1993). ISBN 0-387-94007-3/hbk

This is the second Springer-Verlag edition. The first Springer-Verlag edition from 1986 was very thoroughly and positively reviewed in (1986; Zbl 0588.22001). Meanwhile in 1989 there was published the Russian translation (edited by A. B. Shabat) by Mir, Moscow (1989; Zbl 0743.58003).\par From the author's Preface to the second Springer-Verlag edition.: ``The one substantial addition to the second edition is a short presentation of the calculus of pseudo-differential operators and their use in Shabat's theory of formal symmetries, which provides a powerful, algorithmic method for determining the integrability of evolution equations''.
[Antonín Vaněček (Praha)]
MSC 2000:
*58-02 Research monographs (global analysis)
35-02 Research monographs (partial differential equations)
58J70 Invariance and symmetry properties
35A30 Geometric theory for PDE, transformations
35Q53 KdV-like equations
58J40 Pseudodifferential and Fourier integral operators on manifolds
35K05 Heat equation
35S05 General theory of pseudodifferential operators
22E70 Appl. of Lie groups to physics

Keywords: classical equations of mathematical physics; partial differential equations; symmetry groups; ordinary differential equations; Euler ideal fluid equation; algebraic manipulation; Korteweg-de Vries equation; dimensional analysis; conservation laws; calculus of variations; nonlinear wave equation; Burgers' equation; sine-Gordon equation; Hamiltonian systems; symplectic structure; evolution equations; MACSYMA; symmetries of differential equations; Lie groups; applications; pseudo-differential operators; evolution equations

Citations: Zbl 0588.22001; Zbl 0743.58003

Cited in: Zbl 1247.34052 Zbl 1216.35007 Zbl 1129.34027 Zbl 1024.58006 Zbl 1014.34027 Zbl 0937.58026

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Highlights
Scientific prize winners of the ICM 2010
Overhang
Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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