NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (1), P. 24–28
Stationary nonlinear Schrödinger equation on the graph for the triangle with outgoing bonds
K. K. Sabirov – Turin Polytechnic University in Tashkent; Tashkent University of Information Technologies, Amir Temur Str. 108, Tashkent, Uzbekistan; email@example.com
M. Aripov – Department of Mathematics, National University of Uzbekistan, University Str. 1, 100174, Tashkent, Uzbekistan
D. B. Sagdullayev – Department of High Matnematics, Tashkent State University of Economy, Uzbekistan Str., 49, 100003, Tashkent, Uzbekistan
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 non-linearity.
Keywords: Nonlinear Schrödinger equation, a metric graph, repulsive nonlinearity.