Building extended resolvent of heat operator via twisting transformations

Abstract

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.

15 pages, 2 figures

References in corpus (1)

• Classification of the line-soliton solutions of KPII

Cited by in corpus (9)

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• Extended resolvent of heat operator with multisoliton potential
• Cauchy--Jost function and hierarchy of integrable equations
• Two-dimensional reductions of the Whitham modulation system for the Kadomtsev-Petviashvili equation
• IST of KPII equation for perturbed multisoliton solutions