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. (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”.

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”.

Reviewer: Antonín Vaněček (Praha)

##### MSC:

58-02 | Research exposition (monographs, survey articles) pertaining to global analysis |

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

58J70 | Invariance and symmetry properties for PDEs on manifolds |

35A30 | Geometric theory, characteristics, transformations in context of PDEs |

35Q53 | KdV equations (Korteweg-de Vries equations) |

58J40 | Pseudodifferential and Fourier integral operators on manifolds |

35K05 | Heat equation |

35S05 | Pseudodifferential operators as generalizations of partial differential operators |

22E70 | Applications of Lie groups to the sciences; explicit representations |