On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

被引：1
|
作者：
Prykarpatskyy, Yarema [1 ]
机构：
[1] Agr Univ Krakow, Dept Appl Math, PL-30059 Krakow, Poland
来源：
SYMMETRY-BASEL | 2020年 / 12卷 / 05期
关键词：
Lax-Sato compatibility equations; Chaplygin type hydrodynamical equations; Casimir invariants; torus diffeomorphisms; loop Lie algebra; Lie-Poisson structure; 17B68; 17B80; 35Q53; 35G25; 35N10; 37K35; 58J70; 58J72; 34A34; 37K05; 37K10;
D O I：
10.3390/sym12050697
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页数：9
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