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On the extended resolvent of the nonstationary Schrödinger operator for a Darboux transformed potential. (English) Zbl 1091.81015
Authors’ summary: In the framework of the resolvent approach, a so-called twisting operator is introduced that is able, at the same time, to superimpose à la Darboux \(N\) solitons to a general smooth decaying potential of the nonstationary Schrödinger 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.
Reviewer: Ma Wen-Xiu (Tampa)

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q51 Soliton equations
35Q40 PDEs in connection with quantum mechanics
81R12 Groups and algebras in quantum theory and relations with integrable systems
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