On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

Yarema A. Prykarpatskyy

Abstract

A class of spatially one-dimensional completely integrable Chaplygin hydrodynamic systems was studied within framework of Lie-algebraic approach. The Chaplygin hydrodynamic systems were considered as differential systems on the torus. It has been shown that the geometric structure of the systems under analysis has strong relationship with diffeomorphism group orbits on them. It has allowed to find a new infinite hierarchy of integrable Chaplygin like hydrodynamic systems.
Author Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
Journal seriesSymmetry-Basel, [Symmetry], ISSN 2073-8994, (N/A 70 pkt)
Issue year2020
Vol12
No5
Pages1-9
Publication size in sheets0.5
Article number697
Keywords in English Lax-Sato compatibility equations; Chaplygin type hydrodynamical equations; Casimir invariants; torus diffeomorphisms; loop Lie algebra; Lie-Poisson structure
ASJC Classification1601 Chemistry (miscellaneous); 1701 Computer Science (miscellaneous); 2600 General Mathematics; 3101 Physics and Astronomy (miscellaneous)
DOIDOI:10.3390/sym12050697
URL https://www.mdpi.com/2073-8994/12/5/697
Languageen angielski
LicenseJournal (articles only); author's original; Uznanie Autorstwa (CC-BY); after publication
File
symmetry-12-00697 (1).pdf 239,91 KB
Score (nominal)70
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.64; WoS Impact Factor: 2018 = 2.143 (2) - 2018=2.041 (5)
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