Preprint A100/2001
Huygens' Principle, Dirac Operators, and Rational Solutions of the AKNS Hierarchy

Jorge P. Zubelli | Chalub, Fabio A. C. C.

**Keywords: **
Huygens' Principle | Dirac Operators | rational solutions of the AKNS Hirarchy

We prove that rational solutions
of the AKNS hierarchy of the form $q=\sigma/\tau$ and $r=\rho/\tau$,
where $(\sigma, \tau, \rho)$ are certain Schur functions,
naturally yield Dirac operators of strict Huygens' type, i.e.,
the support of their fundamental solutions is
precisely the surface of the light cone.
This generalizes to the rational solutions of the
AKNS hierarchy a result of
Lagnese and Stellmacher that concerns the rational solutions of the KdV
hierarchy.