K. K. Sabirov, M. Aripov, D. B. Sagdullayev, “Stationary nonlinear Schrödinger equation on the graph for the triangle with outgoing bonds”, Nanosystems: Physics, Chemistry, Mathematics, 2017, Volume 8, Issue 1,Pages <nobr>24

This article is cited in 1 paper

MATHEMATICS

Stationary nonlinear Schrödinger equation on the graph for the triangle with outgoing bonds

K. K. Sabirov^ab, M. Aripov^c, D. B. Sagdullayev^d

^a Turin Polytechnic University in Tashkent
^b Tashkent University of Information Technology, Amir Temur Str. 108, Tashkent, Uzbekistan
^c Department of Mathematics, National University of Uzbekistan, University Str. 1, 100174, Tashkent, Uzbekistan
^d Department of High Matnematics, Tashkent State University of Economy, Uzbekistan Str., 49, 100003, Tashkent, Uzbekistan

Abstract: We consider the stationary (cubic) nonlinear Schrödinger equation (NLSE) on a simple metric graph in the form of a triangle with three infinite outgoing bonds. Exact solutions are obtained for primary star graph with the boundary vertex conditions providing the wave function weights continuity and flux conservation for the case of repulsive nonlinearity.

Keywords: Nonlinear Schrödinger equation, a metric graph, repulsive nonlinearity.

PACS: 05.45.Yv

Received: 10.07.2016
Revised: 25.08.2016

Language: English

DOI: 10.17586/2220-8054-2017-8-1-24-28