New fractional nonlinear integrable Hamiltonian systems
Authors:
- Oksana Ye. Hentosh,
- Bohdan Yu. Kyshakevych,
- Denis Blackmore,
- Anatolij K. Prykarpatski
Abstract
We have constructed a new fractional pseudo-differential metrized operator Lie algebra on the axis, enabling within the general Adler–Kostant–Symes approach the generation of infinite hierarchies of integrable nonlinear differential-fractional Hamiltonian systems of Korteweg–de Vries, Schrödinger and Kadomtsev–Petviashvili types. Using the natural quasi-classical approximation of the metrized fractional pseudo-differential operator Lie algebra, we construct a new metrized fractional symbolic Lie algebra and related infinite hierarchies of integrable mutually commuting fractional symbolic Hamiltonian flows, modeling Benney type hydrodynamical systems.
- Record ID
- CUTaab8f6936b2e471f8099f4591e7ede1c
- Publication categories
- ;
- Author
- Journal series
- Applied Mathematics Letters, ISSN 0893-9659
- Issue year
- 2019
- Vol
- 88
- Pages
- 41-49
- Other elements of collation
- Bibliografia (na s.) - 48-49; Bibliografia (liczba pozycji) - 36; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 88
- Keywords in English
- fractional pseudo-differential metrized operator Lie algebra, fractional symbolic metrized functional Lie algebra, ad-invariant trace-functional, R-structure, Adler–Kostant–Symes approach, Lie–Poisson structure, Casimir invariants, fractional Korteweg–de Vries type equations, fractional nonlinear Schrödinger type equations
- DOI
- DOI:10.1016/j.aml.2018.08.009 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S089396591830288X Opening in a new tab
- Related project
- Teoria równań i nierówności różniczkowych, układy dynamiczne na rozmaitościach, wybrane działy: analizy matematycznej topologii algebry i geometrii oraz probabilistyki teorii grafów i liczb. . Project leader at PK: , ,
Działalność statutowa - Language
- eng (en) English
- Score (nominal)
- 100
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTaab8f6936b2e471f8099f4591e7ede1c/
- URN
urn:pkr-prod:CUTaab8f6936b2e471f8099f4591e7ede1c
* 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.