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TMF, 2019, Volume 201, Number 3, Pages 415–423 (Mi tmf9653)  

Solutions of the discrete nonlinear Schrödinger equation with a trap

V. N. Likhachev, G. A. Vinogradov

Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, Russia

Abstract: We obtain solutions of the discrete nonlinear Schrödinger equation with an impurity center in two ways. In the first of them, we construct the wave function as a series in a certain parameter. In the second, approximate method, we obtain the wave function in the continuum limit. We compare the obtained solutions with numerical results, and the relative accuracy of the solution in the form of a series does not exceed $10^{-15}$ in order of magnitude.

Keywords: discrete nonlinear Schrödinger equation, tight-binding approximation.

DOI: https://doi.org/10.4213/tmf9653

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English version:
Theoretical and Mathematical Physics, 2019, 201:3, 1771–1778

Received: 15.11.2018
Revised: 18.06.2019

Citation: V. N. Likhachev, G. A. Vinogradov, “Solutions of the discrete nonlinear Schrödinger equation with a trap”, TMF, 201:3 (2019), 415–423; Theoret. and Math. Phys., 201:3 (2019), 1771–1778

Citation in format AMSBIB
\Bibitem{LikVin19}
\by V.~N.~Likhachev, G.~A.~Vinogradov
\paper Solutions of the~discrete nonlinear Schr\"odinger equation with a~trap
\jour TMF
\yr 2019
\vol 201
\issue 3
\pages 415--423
\mathnet{http://mi.mathnet.ru/tmf9653}
\crossref{https://doi.org/10.4213/tmf9653}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 3
\pages 1771--1778
\crossref{https://doi.org/10.1134/S0040577919120080}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077537444}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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