Heat operator with pure soliton potential: properties of Jost and dual Jost solutions
arXiv:1105.3681 · doi:10.1063/1.3621715
Abstract
Properties of Jost and dual Jost solutions of the heat equation, $Φ(x,k)$ and $Ψ(x,k)$, in the case of a pure solitonic potential are studied in detail. We describe their analytical properties on the spectral parameter $k$ and their asymptotic behavior on the $x$-plane and we show that the values of $e^{-qx}Φ(x,k)$ and the residua of $e^{qx}Ψ(x,k)$ at special discrete values of $k$ are bounded functions of $x$ in a polygonal region of the $q$-plane. Correspondingly, we deduce that the extended version $L(q)$ of the heat operator with a pure solitonic potential has left and right annihilators for $q$ belonging to these polygonal regions.
26 pages, 3 figures