Journal of Siberian Federal University. Mathematics & Physics / Unified Transform method for the Schr¨odinger Equation on a Simple Metric Graph

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2019 12 (4)
Authors
Khudayberganov, Gulmirza; Sobirov, Zarifboy A.; Eshimbetov, Mardonbek R.
Contact information
Khudayberganov, Gulmirza: National University of Uzbekistan Universitet Str. 4, Tashkent, 100174 Uzbekistan; ; Sobirov, Zarifboy A.: National University of Uzbekistan Universitet Str. 4, Tashkent, 100174 Uzbekistan; ; Eshimbetov, Mardonbek R.: National University of Uzbekistan Universitet Str. 4, Tashkent, 100174 Uzbekistan;
Keywords
Schr¨odinger equation; metric graph; branched structure; unified transform; initial problem; Fourier transform; boundary value problem
Abstract

Integral-representation of solutions of the initial-boundary value problems for the Schr¨odinger equation on simple metric graphs was obtained with the use of the Fokas method. This method uses special gen- eralization 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

Pages
412–420
DOI
10.17516/1997-1397-2019-12-4-412-420
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/111808