Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems

We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems. The nonlocalities considered are reverse-space, reverse-time and reverse-spacetime, each of which can involve either the transpose or the Hermit...

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Autor principal:	Wen-Xiu Ma
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Matrix spectral problem Nonlocal integrable reduction Liouville integrability Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/1fe9b55b5c294e539dc28d9c7da6659e
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spelling	oai:doaj.org-article:1fe9b55b5c294e539dc28d9c7da6659e2021-11-20T05:15:09ZNonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems2666-818110.1016/j.padiff.2021.100190https://doaj.org/article/1fe9b55b5c294e539dc28d9c7da6659e2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666818121000991https://doaj.org/toc/2666-8181We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems. The nonlocalities considered are reverse-space, reverse-time and reverse-spacetime, each of which can involve either the transpose or the Hermitian transpose. The associated spectral problems are used to formulate a kind of Riemann–Hilbert problems and thus inverse scattering transforms. Soliton solutions are generated from specific Riemann–Hilbert problems with the identity jump matrix. We focus on two expository examples: nonlocal PT-symmetric matrix nonlinear Schrödinger and modified Korteweg–de Vries equations.Wen-Xiu MaElsevierarticleMatrix spectral problemNonlocal integrable reductionLiouville integrabilityApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100190- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Matrix spectral problem Nonlocal integrable reduction Liouville integrability Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Matrix spectral problem Nonlocal integrable reduction Liouville integrability Applied mathematics. Quantitative methods T57-57.97 Wen-Xiu Ma Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
description	We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems. The nonlocalities considered are reverse-space, reverse-time and reverse-spacetime, each of which can involve either the transpose or the Hermitian transpose. The associated spectral problems are used to formulate a kind of Riemann–Hilbert problems and thus inverse scattering transforms. Soliton solutions are generated from specific Riemann–Hilbert problems with the identity jump matrix. We focus on two expository examples: nonlocal PT-symmetric matrix nonlinear Schrödinger and modified Korteweg–de Vries equations.
format	article
author	Wen-Xiu Ma
author_facet	Wen-Xiu Ma
author_sort	Wen-Xiu Ma
title	Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
title_short	Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
title_full	Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
title_fullStr	Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
title_full_unstemmed	Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
title_sort	nonlocal pt-symmetric integrable equations and related riemann–hilbert problems
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/1fe9b55b5c294e539dc28d9c7da6659e
work_keys_str_mv	AT wenxiuma nonlocalptsymmetricintegrableequationsandrelatedriemannhilbertproblems
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Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems

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