Geodesic
Solutions of the~discrete nonlinear Schr\"odinger equation with a~trap
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 415-423

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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. 
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     author = {V. N. Likhachev and G. A. Vinogradov},
     title = {Solutions of the~discrete nonlinear {Schr\"odinger} equation with a~trap},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {415--423},
     publisher = {mathdoc},
     volume = {201},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a7/}
}
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V. N. Likhachev; G. A. Vinogradov. Solutions of the~discrete nonlinear Schr\"odinger equation with a~trap. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 415-423. http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a7/