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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (6), P. 757-761

Linearized KdV equation on a metric graph

Z. A. Sobirov – Faculty of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, 100047 Tashkent; Applied Mathematics Department of Tashkent Financial Institute, 100000 Tashkent, Uzbekistan; sobirovzar@gmail.com
M. I. Akhmedov – Applied Mathematics Department of Tashkent Financial Institute, 100000 Tashkent, Uzbekistan
O. V. Karpova – Faculty of Physics, National University of Uzbekistan, Vuzgorodok, 100047 Tashkent; Turin Polytechnic University in Tashkent, Uzbekistan; ola_july@mail.ru
B. Jabbarova – Urganch State University, Urganch, Uzbekistan

We address a linearized KdV equation on metric star graphs with one incoming nite bond and two outgoing semi-innite bonds. Using the theory of potentials, we reduce the problem to systems of linear integral equations and show that they are uniquely solvable under conditions of the uniqueness theorem.

Keywords: KdV, IBVP, PDE on metric graphs, exact solution, third order dierential equations.

PACS 02.30.Ik, 05.45.Yv

DOI 10.17586/2220-8054-2015-6-6-757-761

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