Building extended resolvent of heat operator via twisting transformations

Details Building extended resolvent of heat operator via twisting transformations Building extended resolvent of heat operator via twisting transformations

2009-01-24

arxiv.org/abs/0901.3857v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 2 figures

Scientific paper

Twisting transformations for the heat operator are introduced. They are used, at the same time, to superimpose a` la Darboux N solitons to a generic smooth, decaying at infinity, potential and to generate the corresponding Jost solutions. These twisting operators are also used to study the existence of the related extended resolvent. Existence and uniqueness of the extended resolvent in the case of $N$ solitons with N "ingoing" rays and one "outgoing" ray is studied in details.

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