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Zap. Nauchn. Sem. POMI, 2010, Volume 374, Pages 107–120 (Mi znsl3597)  

On spectral curve for functional-difference Shrödinger equation

G. M. Golovachev, A. O. Smirnov

St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia

Abstract: The method of construction some set of finite-gap solutions of functional-difference deformation Shrödinger equation $v(x)f(x+2h)+f(x)=\lambda f(x+h)$ is offered. It is shown that edges of gaps of corresponding spectral curve depend on $x$. Examples are given. Bibl. – 7 titles.

Key words and phrases: finite-gap solution, difference equation, functional-difference equation, spectral curve.

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English version:
Journal of Mathematical Sciences (New York), 2010, 168:6, 820–828

UDC: 517.9
Received: 09.03.2010

Citation: G. M. Golovachev, A. O. Smirnov, “On spectral curve for functional-difference Shrödinger equation”, Questions of quantum field theory and statistical physics. Part 21, Zap. Nauchn. Sem. POMI, 374, POMI, St. Petersburg, 2010, 107–120; J. Math. Sci. (N. Y.), 168:6 (2010), 820–828

Citation in format AMSBIB
\Bibitem{GolSmi10}
\by G.~M.~Golovachev, A.~O.~Smirnov
\paper On spectral curve for functional-difference Shr\"odinger equation
\inbook Questions of quantum field theory and statistical physics. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 374
\pages 107--120
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3597}
\elib{https://elibrary.ru/item.asp?id=15330992}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 168
\issue 6
\pages 820--828
\crossref{https://doi.org/10.1007/s10958-010-0030-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77955273298}


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