Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons

M. E. Akramov; J. R. Yusupov; M. Ehrhardt; H. Susanto; D. U. Matrasulov

doi:10.1016/j.physleta.2022.128611

Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons

M. E. Akramov
, J. R. Yusupov
, M. Ehrhardt
, H. Susanto
, D. U. Matrasulov

Mathematics

National University of Uzbekistan named after Mirzo Ulugbek
Yeoju Technical Institute in Tashkent
Bergische Universität Wuppertal
Turin Polytechnic University in Tashkent

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9 Scopus citations

Abstract

We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schrödinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.

Original language	British English
Article number	128611
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	459
DOIs	https://doi.org/10.1016/j.physleta.2022.128611
State	Published - 29 Jan 2023

Keywords

Nonlocal nonlinear Schrödinger equation
PT-symmetric solitons
Transparent boundary conditions

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10.1016/j.physleta.2022.128611

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Akramov, M. E., Yusupov, J. R., Ehrhardt, M., Susanto, H., & Matrasulov, D. U. (2023). Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons. Physics Letters, Section A: General, Atomic and Solid State Physics, 459, Article 128611. https://doi.org/10.1016/j.physleta.2022.128611

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abstract = "We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schr{\"o}dinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schr{\"o}dinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.",

keywords = "Nonlocal nonlinear Schr{\"o}dinger equation, PT-symmetric solitons, Transparent boundary conditions",

author = "Akramov, \{M. E.\} and Yusupov, \{J. R.\} and M. Ehrhardt and H. Susanto and Matrasulov, \{D. U.\}",

note = "Funding Information: The work is supported by the grant of the Ministry for Innovation Development of Uzbekistan (Ref. No. F-2021-440). One of the authors (DM) thanks the Associates Program of the Abdus Salam ICTP for his hospitality during his visit. H.S. also acknowledges support from Khalifa University through a Faculty Start-Up Grant (No. 8474000351/FSU-2021-011). Funding Information: The work is supported by the grant of the Ministry for Innovation Development of Uzbekistan (Ref. No. F-2021-440 ). One of the authors (DM) thanks the Associates Program of the Abdus Salam ICTP for his hospitality during his visit. H.S. also acknowledges support from Khalifa University through a Faculty Start-Up Grant (No. 8474000351/FSU-2021-011 ). Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

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doi = "10.1016/j.physleta.2022.128611",

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Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons. / Akramov, M. E.; Yusupov, J. R.; Ehrhardt, M. et al.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 459, 128611, 29.01.2023.

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

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AU - Yusupov, J. R.

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AU - Susanto, H.

AU - Matrasulov, D. U.

N1 - Funding Information: The work is supported by the grant of the Ministry for Innovation Development of Uzbekistan (Ref. No. F-2021-440). One of the authors (DM) thanks the Associates Program of the Abdus Salam ICTP for his hospitality during his visit. H.S. also acknowledges support from Khalifa University through a Faculty Start-Up Grant (No. 8474000351/FSU-2021-011). Funding Information: The work is supported by the grant of the Ministry for Innovation Development of Uzbekistan (Ref. No. F-2021-440 ). One of the authors (DM) thanks the Associates Program of the Abdus Salam ICTP for his hospitality during his visit. H.S. also acknowledges support from Khalifa University through a Faculty Start-Up Grant (No. 8474000351/FSU-2021-011 ). Publisher Copyright: © 2023 Elsevier B.V.

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N2 - We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schrödinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.

AB - We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schrödinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.

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ER -

Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons

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