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

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

Mathematics

National University of Uzbekistan named after Mirzo Ulugbek
Tashkent University of Information Technologies named after Muhammad al-Khwarizmi
Turin Polytechnic University in Tashkent
Yeoju Technical Institute in Tashkent

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 language	British English
Article number	054205
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	105
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevE.105.054205
State	Published - May 2022

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Akramov, M., Sabirov, K., Matrasulov, D., Susanto, H., Usanov, S., & Karpova, O. (2022). Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 105(5), Article 054205. https://doi.org/10.1103/PhysRevE.105.054205

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title = "Nonlocal nonlinear Schr{\"o}dinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks",

abstract = "We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schr{\"o}dinger 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 Schr{\"o}dinger 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.",

author = "M. Akramov and K. Sabirov and D. Matrasulov and H. Susanto and S. Usanov and O. Karpova",

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Akramov, M, Sabirov, K, Matrasulov, D, Susanto, H, Usanov, S & Karpova, O 2022, 'Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks', Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 105, no. 5, 054205. https://doi.org/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. / Akramov, M.; Sabirov, K.; Matrasulov, D. et al.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 105, No. 5, 054205, 05.2022.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Nonlocal nonlinear Schrödinger equation on metric graphs

T2 - A model for generation and transport of parity-time-symmetric nonlocal solitons in networks

AU - Akramov, M.

AU - Sabirov, K.

AU - Matrasulov, D.

AU - Susanto, H.

AU - Usanov, S.

AU - Karpova, O.

PY - 2022/5

Y1 - 2022/5

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85131294816

U2 - 10.1103/PhysRevE.105.054205

DO - 10.1103/PhysRevE.105.054205

M3 - Article

C2 - 35706170

AN - SCOPUS:85131294816

SN - 1539-3755

VL - 105

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 5

M1 - 054205

ER -

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

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