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

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.

26 pages, 3 figures

References in corpus (3)

• KP solitons in shallow water
• On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
• Building extended resolvent of heat operator via twisting transformations

Cited by in corpus (4)

• The direct scattering problem for perturbed Kadomtsev-Petviashvili multi line solitons
• Extended resolvent of heat operator with multisoliton potential
• The direct problem for the perturbed Kadomtsev-Petviashvili II one line solitons
• IST of KPII equation for perturbed multisoliton solutions