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Applications of Lie groups to differential equations. 2nd ed. (English) Zbl 0785.58003
Graduate Texts in Mathematics. 107. New York: Springer-Verlag. xxviii, 513 p. DM 108.00; sfr 108.00 (1993).
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). 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”.

58-02Research monographs (global analysis)
35-02Research monographs (partial differential equations)
58J70Invariance and symmetry properties
35A30Geometric theory for PDE, characteristics, transformations
35Q53KdV-like (Korteweg-de Vries) equations
58J40Pseudodifferential and Fourier integral operators on manifolds
35K05Heat equation
35S05General theory of pseudodifferential operators
22E70Applications of Lie groups to physics; explicit representations