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

M. Boiti, F. Pempinelli, A. K. Pogrebkov

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4 Citations (Scopus)

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-qxΦ(x, k) and the residues of eqxΨ(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.

Original languageEnglish
Article number083506
JournalJournal of Mathematical Physics
Volume52
Issue number8
DOIs
Publication statusPublished - 4 Aug 2011

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