Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks

M Akramov; K Sabirov; D Matrasulov; H Susanto; S Usanov; O Karpova

doi:10.1103/PhysRevE.105.054205

Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks

Phys Rev E. 2022 May;105(5-1):054205. doi: 10.1103/PhysRevE.105.054205.

Authors

M Akramov¹, K Sabirov², D Matrasulov³, H Susanto⁴, S Usanov⁵, O Karpova³

Affiliations

¹ Physics Department, National University of Uzbekistan, Vuzgorodok, Tashkent 100174, Uzbekistan.
² Tashkent University of Information Technology, Amir Temur Avenue 108, Tashkent 100200, Uzbekistan.
³ Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent, 17 Niyazov Street, 100095 Tashkent, Uzbekistan.
⁴ Department of Mathematics, Khalifa University, Abu Dhabi Campus, PO Box 127788, United Arab Emirates.
⁵ Physics Department, Yeoju Technical Institute in Tashkent, 156 Usman Nasyr Street, 100121 Tashkent, Uzbekistan.

PMID: 35706170
DOI: 10.1103/PhysRevE.105.054205

Abstract

We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schrödinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for the simplest graph topologies, such as star and tree graphs. The integrability of the problem is shown by proving the existence of an infinite number of conservation laws. A model for soliton generation in such PT-symmetric optical fibers and their networks governed by the nonlocal nonlinear Schrödinger equation is proposed. Exact formulas for the number of generated solitons are derived for the cases when the problem is integrable. Numerical solutions are obtained for the case when integrability is broken.