72 research outputs found
Properties of the solitonic potentials of the heat operator
Properties of the pure solitonic -function and potential of the heat
equation are studied in detail. We describe the asymptotic behavior of the
potential and identify the ray structure of this asymptotic behavior on the
-plane in dependence on the parameters of the potential
Towards spectral theory of the Nonstationary Schr\"{o}dinger equation with a two-dimensionally perturbed one-dimensional potential
The Nonstationary Schr\"{o}dinger equation with potential being a
perturbation of a generic one-dimensional potential by means of a decaying
two-dimensional function is considered here in the framework of the extended
resolvent approach. The properties of the Jost solutions and spectral data are
investigated.Comment: 22 pages, no figure
On the extended resolvent of the Nonstationary Schrodingher operator for a Darboux transformed potential
In the framework of the resolvent approach it is introduced a so called
twisting operator that is able, at the same time, to superimpose \`a la Darboux
solitons to a generic smooth decaying potential of the Nonstationary
Schr\"odinger operator and to generate the corresponding Jost solutions. This
twisting operator is also used to construct an explicit bilinear representation
in terms of the Jost solutions of the related extended resolvent. The main
properties of the Jost and auxiliary Jost solutions and of the resolvent are
discussed.Comment: 24 pages, class files from IO
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