A discrete nonlinear Schrödinger-type hierarchy, its finite-dimensional reduction analysis, and the numerical integration scheme
Authors:
- A. K. Prykarpatski,
- J. L. Cieśliński
Abstract
We investigate the procedures of discretization of the integrable nonlinear Schrödinger dynamical system, well known as the Ablowitz–Ladik equation, the corresponding symplectic structures, and the finite-dimensional invariant reductions. We develop an efficient scheme of invariant reduction of the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter. We construct a finite set of recurrence algebraic regular relations that allows one to generate solutions of the discrete nonlinear Schrödinger dynamical system and discuss the related functional spaces of solutions. Finally, we analyze the Fourier-transform approach to the study of the set of solutions of the discrete nonlinear Schrödinger dynamical system and its functional-analytic aspects.
- Record ID
- CUT0fb9ffe6e38d4199a61f4b42e4941e58
- Publication categories
- ;
- Author
- Journal series
- Journal of Mathematical Sciences, ISSN 1072-3374
- Issue year
- 2018
- Vol
- 231
- No
- 6
- Pages
- 779-819
- Other elements of collation
- Bibliografia (na s.) - 817-819; Bibliografia (liczba pozycji) - 61; Oznaczenie streszczenia - Streszcz. ang.; Numeracja w czasopiśmie - Vol. 231, No. 6
- Substantive notes
- Informacja na publikacji: Published in Neliniini Kolyvannya, Vol. 20, No. 2, pp. 228–266, April–June, 2017.
- Keywords in English
- nonlinear dynamical systems, integrability, reduction
- DOI
- DOI:10.1007/s10958-018-3850-9 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s10958-018-3850-9 Opening in a new tab
- Related project
- Dyskretyzacje układów dynamicznych zachowujące całki ruchu. . Project leader at PK: , ,
- Language
- eng (en) English
- License
- Score (nominal)
- 0
- Additional fields
- Indeksowana w: Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT0fb9ffe6e38d4199a61f4b42e4941e58/
- URN
urn:pkr-prod:CUT0fb9ffe6e38d4199a61f4b42e4941e58
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.