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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (2), P. 162–172

A solution of nonlinear Schrödinger equation on metric graphs

K. K. Sabirov – National University of Uzbekistan, 4 University St., 100074, Tashkent, Uzbekistan; karimjonsabirov@yahoo.com
A. R. Khalmukhamedov – Tashkent branch of Moscow State University named after L. V. Lomonosov, 22 Amir Temur St., 100060, Tashkent, Uzbekistan

We treat the Nonlinear Schrödinger equation (NLSE) on Metric graph. An approach developed earlier for NLSE on interval [14], is extended for star graph. Dirichlet boundary conditions are imposed at the ends of bonds are imposed, while continuity conditions are chosen at the vertex of graph.

Keywords: metric graphs, nonlinear Schrödinger equation, solitons.

PACS 02.30.Jr,02.30.Ik

DOI 10.17586/2220-8054-2015-6-2-162-172

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