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The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme

The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme

We investigate discretizations of the integrable nonlinear Schrodinger dynamical system, well known as the ¨ Ablowitz – Ladik equation, the related symplectic structures and its finite dimensional invariant reductions. An effective scheme of invariant reducing the corresponding infinite system of or...

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Main Authors: Prykarpatsky, A.K., Cieśliński, J.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Нелінійні коливання
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/177304
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spelling irk-123456789-1773042021-02-15T01:26:50Z The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme Prykarpatsky, A.K. Cieśliński, J. We investigate discretizations of the integrable nonlinear Schrodinger dynamical system, well known as the ¨ Ablowitz – Ladik equation, the related symplectic structures and its finite dimensional invariant reductions. An effective scheme of invariant reducing the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter is developed. A finite set of recurrent algebraic regular relations, allowing to generate solutions of the discrete nonlinear Schrodinger dynamical system, is constructed, the related functional spaces of ¨ solutions is discussed. Finally, the Fourier transform approach to studying the solution set of the discrete nonlinear Schrodinger dynamical system and its functional-analytical aspects is analyzed. Дослiджуються дискретизацiї iнтегровної нелiнiйної динамiчної системи Шрьодiнгера, вiдомої як рiвняння Абловiца – Ладiка, вiдповiднi симплектичнi структури та її скiнченновимiрнi iнварiантнi редукцiї. Побудовано ефективний алгоритм iнварiантної редукцiї вiдповiдної нескiнченної системи звичайних диференцiальних рiвнянь до еквiвалентної скiнченної системи звичайних диференцiальних рiвнянь вiдносно параметра еволюцiї. Побудовано скiнченну множину рекурентних алгебраїчних регулярних спiввiдношень, що дозволило побудувати розв’язки дискретної нелiнiйної динамiчної системи Шрьодiнгера, та розглянуто вiдповiднi функцiональнi простори розв’язкiв. Проведено аналiз пiдходу перетворення Фур’є до вивчення множини розв’язкiв дискретної нелiнiйної динамiчної системи Шрьодiнгера та її функцiонально-аналiтичних аспектiв. 2017 Article The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme / A.K. Prykarpatsky, J. Cieśliński // Нелінійні коливання. — 2017. — Т. 20, № 2. — С. 228-266 — Бібліогр.: 61 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/177304 517.9 en Нелінійні коливання Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We investigate discretizations of the integrable nonlinear Schrodinger dynamical system, well known as the ¨ Ablowitz – Ladik equation, the related symplectic structures and its finite dimensional invariant reductions. An effective scheme of invariant reducing the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter is developed. A finite set of recurrent algebraic regular relations, allowing to generate solutions of the discrete nonlinear Schrodinger dynamical system, is constructed, the related functional spaces of ¨ solutions is discussed. Finally, the Fourier transform approach to studying the solution set of the discrete nonlinear Schrodinger dynamical system and its functional-analytical aspects is analyzed.
format Article
author Prykarpatsky, A.K.
Cieśliński, J.
spellingShingle Prykarpatsky, A.K.
Cieśliński, J.
The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
Нелінійні коливання
author_facet Prykarpatsky, A.K.
Cieśliński, J.
author_sort Prykarpatsky, A.K.
title The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
title_short The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
title_full The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
title_fullStr The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
title_full_unstemmed The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
title_sort discrete nonlinear schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/177304
citation_txt The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme / A.K. Prykarpatsky, J. Cieśliński // Нелінійні коливання. — 2017. — Т. 20, № 2. — С. 228-266 — Бібліогр.: 61 назв. — англ.
series Нелінійні коливання
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AT cieslinskij thediscretenonlinearschrodingertypehierarchyitsfinitedimensionalreductionanalysisandnumericalintegrabilityscheme
AT prykarpatskyak discretenonlinearschrodingertypehierarchyitsfinitedimensionalreductionanalysisandnumericalintegrabilityscheme
AT cieslinskij discretenonlinearschrodingertypehierarchyitsfinitedimensionalreductionanalysisandnumericalintegrabilityscheme
first_indexed 2023-10-18T22:43:16Z
last_indexed 2023-10-18T22:43:16Z
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