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

Research output: Contribution to journalArticlepeer-review

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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.

Original languageBritish English
Article number054205
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume105
Issue number5
DOIs
StatePublished - May 2022

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