Huygens' Principle, Dirac Operators, and Rational Solutions of the AKNS Hierarchy
Jorge P. Zubelli | Chalub, Fabio A. C. C.
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.