Acta Applicandae Mathematica

, Volume 53, Issue 2, pp 125–185

Hierarchies of Huygens' Operators and Hadamard's Conjecture

  • Yuri Berest

DOI: 10.1023/A:1006069012474

Cite this article as:
Berest, Y. Acta Applicandae Mathematicae (1998) 53: 125. doi:10.1023/A:1006069012474


We develop a new unified approach to the problem of constructing linear hyperbolic partial differential operators that satisfy Huygens' principle in the sense of J. Hadamard. The underlying method is essentially algebraic and based on a certain nonlinear extension of similarity (gauge) transformations in the ring of analytic differential operators.

The paper provides a systematic and self-consistent review of classical and recent results on Huygens' principle in Minkowski spaces. Most of these results are carried over to more general pseudo-Riemannian spaces with the metric of a plane gravitational wave.

A particular attention is given to various connections of Huygens' principle with integrable systems and the soliton theory. We discuss the link to nonlinear KdV-type evolution equations, Darboux–Bäcklund transformations and the bispectral problem in the sense of Duistermaat, Grünbaum and Wilson.

hyperbolic equations fundamental solutions Huygens' principle lacunas integrable systems nonlinear evolution equations 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Yuri Berest
    • 1
  1. 1.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada

Personalised recommendations