K. K. Sabirov, J. R. Yusupov, Kh. Sh. Matyokubov, H. Susanto, D. U. Matrasulov, “Networks with point-like nonlinearities”, Nanosystems: Physics, Chemistry, Mathematics, 2022, Volume 13, Issue 1,Pages <nobr>30

MATHEMATICS

Networks with point-like nonlinearities

K. K. Sabirov^a, J. R. Yusupov^bc, Kh. Sh. Matyokubov^d, H. Susanto^e, D. U. Matrasulov^f

^a Tashkent University of Information Technologies, 100200, Tashkent, Uzbekistan
^b Yeoju Technical Institute in Tashkent, 100121, Tashkent, Uzbekistan
^c National University of Uzbekistan, 100174, Tashkent, Uzbekistan
^d Urgench State University, 220100, Urgench, Uzbekistan
^e Khalifa University, 127788, Abu Dhabi, UAE
^f Turin Polytechnic University in Tashkent, 100095, Tashkent, Uzbekistan

Abstract: We study static nonlinear waves in networks described by a nonlinear Schrödinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking caused by bifurcations is found.

Keywords: metric graphs, point-like nonlinearity, NLSE, spontaneous symmetry breaking bifurcations.

PACS: 03.75.Lm, 05.45.Yv, 05.45.-a

Received: 24.06.2021
Revised: 30.12.2021
Accepted: 01.02.2022

Language: English

DOI: 10.17586/2220-8054-2022-13-1-30-35