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Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model. (English. Russian original) Zbl 0637.35060
Funct. Anal. Appl. 20, 203-214 (1986); translation from Funkts. Anal. Prilozh. 20, No. 3, 42-54 (1986).
Theorems about expansions in terms of Baker-Akhiezer functions associated with the time-dependent Schrödinger operator \(i\partial_ t-\partial\) \(2_ x+u(x,t)\) are proved. The nonlinear correlation between these functions and the potential u(x,t) are obtained. These results are applied to the construction of the exact solutions of the equations of the time-dependent Peierls model.
Reviewer: M.A.Perelmuter

MSC:
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35C10 Series solutions to PDEs
35J10 Schrödinger operator, Schrödinger equation
35K10 Second-order parabolic equations
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