Hadamard's problem and coxeter groups: New examples of Huygens' equations

  title={Hadamard's problem and coxeter groups: New examples of Huygens' equations},
  author={Yuri Yu. Berest and A P Veselov},
  journal={Functional Analysis and Its Applications},
A central hyperplane arrangement in ℂ2 with multiplicity is called a "locus configuration" if it satisfies a series of "locus equations" on each hyperplane. Following [4], we demonstrate that the
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Abstract Monodromy is the simplest obstruction to the existence of global action–angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with
Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators
In this note, we compute the Hadamard coefficients of algebraically integrable Schrödinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens’
The Lagnese–Stellmacher Potentials Revisited
AbstractWe give a new proof of a classical result of Lagnese and Stellmacher, characterizing all Huygens’ operators of the form $$\frac{\partial^2}{\partial x_{0}^2}-\sum_{i=1}^{2n+3}
Stepwise Gauge Equivalence of Differential Operators
In this paper, we study the relation between the notion of gauge equivalence and solutions of certain systems of nonlinear partial differential equations. This relation is based on stepwise gauge
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The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda $g$-soliton is computed, using Sato theory. The result is used to give an explicit expansion of the
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New examples of iso-Huygens deformations of the ultrahyperbolic operator and its powers with Calogero–Moser and Lagnese–Stellmacher potentials are considered. Bibliography: 12 titles.


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We give examples of finite gap Schrödinger operators in the two-dimensional case.
Deformations preserving Huygens’ principle
A new kind of deformation related to the Korteweg–de Vries hierarchy and its master symmetries is studied. The algebra of deformations is generated by trivial (point) transformations via a special
Shift operators for the quantum Calogero-Sutherland problems via Knizhnik-Zamolodchikov equation
We give a natural interpretation of the shift operators for Calogero-Sutherland quantum problem via KZ equation using Matsuo-Cherednik mappings. The explicit formulas for the inversions of these
Algebraic integrability for the Schrödinger equation and finite reflection groups
Algebraic integrability of ann-dimensional Schrödinger equation means that it has more thann independent quantum integrals. Forn=1, the problem of describing such equations arose in the theory of
A Remark on the Dunkl Differential—Difference Operators
Let E be a Euclidean vector space of dimension n with inner product (·,·). For each α ∈ E with (α, α) = 2 we write $$ {r_{\alpha }}(\lambda ) = \lambda - (\alpha, \lambda )\alpha, \lambda \in E $$
The hierarchy of Huygens equations in spaces with a non-trivial conformal group
CONTENTS Introduction Chapter I. The wave equation in curved spaces § 1. Conformal invariance § 2. The geodesic distance § 3. The Cauchy problem § 4. The Huygens principle Chapter II. Generalization
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There is a theory of spherical harmonics for measures invariant under a finite reflection group. The measures are products of powers of linear functions, whose zero-sets are the mirrors of the
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The sine‐Gordon equations: Complete and partial integrability
  • John Weiss
  • Mathematics
  • 1984
The sine–Gordon equation in one space‐one time dimension is known to possess the Painleve property and to be completely integrable. It is shown how the method of ‘‘singular manifold’’ analysis