This article is cited in 2 papers

Unified transform method for the Schrödinger equation on a simple metric graph

Gulmirza Khudayberganov, Zarifboy A. Sobirov, Mardonbek R. Eshimbetov

National University of Uzbekistan, Universitet Str. 4, Tashkent, 100174, Uzbekistan

Abstract: Integral-representation of solutions of the initial-boundary value problems for the Schrödinger equation on simple metric graphs was obtained with the use of the Fokas method. This method uses special generalization of the Fourier transform that is referred to as the unified transform. Obtained representation of solutions of the problem for open and closed simple star graphs allows one to identify transmitted, reflected and trapped waves at the graph branching point.

Keywords: Schrödinger equation, metric graph, branched structure, unified transform, initial problem, Fourier transform, boundary value problem.

UDC: 517.953

Received: 16.11.2018
Received in revised form: 06.02.2019
Accepted: 05.04.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-4-412-420

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