Huygens' principle and integrability
Abstract
CONTENTS Introduction Chapter I. Hadamard's criterion and the Painlevé property Chapter II. Solution of the Hadamard problem in the four-dimensional Minkowski space §2.1. The Asgeirsson theory and the problem of wave families §2.2. Hadamard's approach. An example of a non-trivial Huygens equation with complex coefficients Chapter III. Examples of Stellmacher-Lagnese Huygens equations §3.1. The examples of Stellmacher §3.2. The hierarchy of Lagnese-Stellmacher Huygens equations and rational solutions of the Korteweg-de Vries equations Chapter IV. A new class of Huygens equations related to the Coxeter groups §4.1. The generalized Calogero problem for particular values of parameters and the Dunkl operators formalism §4.2. Huygens' principle for wave operators with generalized Calogero potentials §4.3. Intertwining operators with a spectral parameter and fundamental solutions of the Huygens equations Chapter V. Wave equations in Riemannian spaces with a non-trivial conformal group Chapter VI. Huygens' principle on symmetric spaces §6.1. Radial components of the Laplace-Beltrami operator and the shift operators §6.2. The fundamental solution for wave equations on symmetric spaces References
- Publication:
-
Russian Mathematical Surveys
- Pub Date:
- December 1994
- DOI:
- 10.1070/RM1994v049n06ABEH002447
- Bibcode:
- 1994RuMaS..49....5B