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.

N1 - Publisher Copyright:
© 2022 American Physical Society.

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 - http://www.scopus.com/inward/record.url?scp=85131294816&partnerID=8YFLogxK

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 -