Formal Diagonalisation of Lax-Darboux Schemes

Formal Diagonalisation of Lax-Darboux Schemes

We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-differe...

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Main Author: A. V. Mikhailov
Format: Article
Language:English
Published: Yaroslavl State University 2015-12-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
formal diagonalisation
lax-darboux schemes
nonlinear schr¨odinger equation
nls
Online Access:https://www.mais-journal.ru/jour/article/view/296
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spelling doaj-9c600b7ee93541a98e8eb3c859c5b60d2021-07-29T08:15:21ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172015-12-0122679581710.18255/1818-1015-2015-6-795-817274Formal Diagonalisation of Lax-Darboux SchemesA. V. Mikhailov0University of Leeds, School of Mathematics (Leeds, UK)We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-difference integrable systems (including the Toda lattice and differential-difference Heisenberg chain) and integrable partial difference systems. We show that there exists a transformation which formally diagonalises all elements of the Lax-Darboux scheme simultaneously. It provides us with generating functions of local conservation laws for all integrable systems obtained. We discuss the relations between conservation laws for systems belonging to the Lax-Darboux scheme.https://www.mais-journal.ru/jour/article/view/296formal diagonalisationlax-darboux schemesnonlinear schr¨odinger equationnls
collection DOAJ
language English
format Article
sources DOAJ
author A. V. Mikhailov
spellingShingle A. V. Mikhailov
Formal Diagonalisation of Lax-Darboux Schemes
Modelirovanie i Analiz Informacionnyh Sistem
formal diagonalisation
lax-darboux schemes
nonlinear schr¨odinger equation
nls
author_facet A. V. Mikhailov
author_sort A. V. Mikhailov
title Formal Diagonalisation of Lax-Darboux Schemes
title_short Formal Diagonalisation of Lax-Darboux Schemes
title_full Formal Diagonalisation of Lax-Darboux Schemes
title_fullStr Formal Diagonalisation of Lax-Darboux Schemes
title_full_unstemmed Formal Diagonalisation of Lax-Darboux Schemes
title_sort formal diagonalisation of lax-darboux schemes
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2015-12-01
description We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-difference integrable systems (including the Toda lattice and differential-difference Heisenberg chain) and integrable partial difference systems. We show that there exists a transformation which formally diagonalises all elements of the Lax-Darboux scheme simultaneously. It provides us with generating functions of local conservation laws for all integrable systems obtained. We discuss the relations between conservation laws for systems belonging to the Lax-Darboux scheme.
topic formal diagonalisation
lax-darboux schemes
nonlinear schr¨odinger equation
nls
url https://www.mais-journal.ru/jour/article/view/296
work_keys_str_mv AT avmikhailov formaldiagonalisationoflaxdarbouxschemes
_version_ 1721256486886178816

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