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arXiv · 1105.3681

Heat operator with pure soliton potential: properties of Jost and dual Jost solutions

M. Boiti·F. Pempinelli·A. Pogrebkov
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Abstract

Properties of Jost and dual Jost solutions of the heat equation, $\Phi(x,k)$ and $\Psi(x,k)$, 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 $e^{-qx}\Phi(x,k)$ and the residua of $e^{qx}\Psi(x,k)$ 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.

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M. Boiti, F. Pempinelli, A. Pogrebkov. 2011-05-18. Heat operator with pure soliton potential: properties of Jost and dual Jost solutions. https://doi.org/10.1063/1.3621715

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