Geodesic
Unified transform method for the Schr\"odinger equation on a simple metric graph
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 412-420

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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, boundary value problem.
Mots-clés : Fourier transform 
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     title = {Unified transform method for the {Schr\"odinger} equation on a simple metric graph},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Gulmirza Khudayberganov; Zarifboy A. Sobirov; Mardonbek R. Eshimbetov. Unified transform method for the Schr\"odinger equation on a simple metric graph. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 412-420. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a1/