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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Yaroslavl State University
2015-12-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/296 |
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| author | A. V. Mikhailov |
| author_facet | A. V. Mikhailov |
| author_sort | A. V. Mikhailov |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9c600b7ee93541a98e8eb3c859c5b60d |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-9c600b7ee93541a98e8eb3c859c5b60d2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-12-0122679581710.18255/1818-1015-2015-6-795-817274Formal 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 |
| spellingShingle | A. V. Mikhailov Formal Diagonalisation of Lax-Darboux Schemes Моделирование и анализ информационных систем formal diagonalisation lax-darboux schemes nonlinear schr¨odinger equation nls |
| title | 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_short | Formal Diagonalisation of Lax-Darboux Schemes |
| title_sort | formal diagonalisation of lax darboux schemes |
| 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 |