Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials have been investigated. However, previous studi...

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Autores principales:	Yong Chen, Zhenya Yan, Dumitru Mihalache, Boris A. Malomed
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9db8612d44a04339bdd928ec0e3c3c75
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spelling	oai:doaj.org-article:9db8612d44a04339bdd928ec0e3c3c752021-12-02T12:31:48ZFamilies of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses10.1038/s41598-017-01401-32045-2322https://doaj.org/article/9db8612d44a04339bdd928ec0e3c3c752017-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01401-3https://doaj.org/toc/2045-2322Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials have been investigated. However, previous studies of $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric Scarf-II potentials. The broken linear $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric ones, but feature similar properties. Our results may suggest new experiments for $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric nonlinear waves in nonlinear nonuniform optical media.Yong ChenZhenya YanDumitru MihalacheBoris A. MalomedNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-21 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Yong Chen Zhenya Yan Dumitru Mihalache Boris A. Malomed Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
description	Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials have been investigated. However, previous studies of $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric Scarf-II potentials. The broken linear $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric ones, but feature similar properties. Our results may suggest new experiments for $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric nonlinear waves in nonlinear nonuniform optical media.
format	article
author	Yong Chen Zhenya Yan Dumitru Mihalache Boris A. Malomed
author_facet	Yong Chen Zhenya Yan Dumitru Mihalache Boris A. Malomed
author_sort	Yong Chen
title	Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
title_short	Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
title_full	Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
title_fullStr	Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
title_full_unstemmed	Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
title_sort	families of stable solitons and excitations in the pt-symmetric nonlinear schrödinger equations with position-dependent effective masses
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/9db8612d44a04339bdd928ec0e3c3c75
work_keys_str_mv	AT yongchen familiesofstablesolitonsandexcitationsintheptsymmetricnonlinearschrodingerequationswithpositiondependenteffectivemasses AT zhenyayan familiesofstablesolitonsandexcitationsintheptsymmetricnonlinearschrodingerequationswithpositiondependenteffectivemasses AT dumitrumihalache familiesofstablesolitonsandexcitationsintheptsymmetricnonlinearschrodingerequationswithpositiondependenteffectivemasses AT borisamalomed familiesofstablesolitonsandexcitationsintheptsymmetricnonlinearschrodingerequationswithpositiondependenteffectivemasses
_version_	1718394295375888384

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

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