Preprint A275/2004
Matrix Bispectrality and Huygens' Principle for Dirac Operators

Jorge Zubelli | Chalub, Fabio

**Keywords: **
Huygens principle; Dirac Operators; Bispectrality; AKNS

We explore relations among Huygens' principle for Dirac operators,
rational solutions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy,
and matrix bispectrality.
We show how such properties are connected by relating
the Hadamard expansion coefficients to the
expressions of the nonlinear AKNS flows.
The matrix properties above have natural scalar counterparts
obtained by reduction to certain manifolds, in which case
we get Huygens' principle for wave operators,
rational solutions of the Korteweg-de Vries equation and
scalar bispectrality. As a by-product we
give an alternative proof to a classical result of Lagnese and
Stellmacher.