On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

Symmetry

Yarema Prykarpatskyy¹ 

[1] Department of Applied Mathematics, University of Agriculture in Krakow, 30-059 Krakow, Poland;

关键词: Lax-Sato compatibility equations;    Chaplygin type hydrodynamical equations;    Casimir invariants;    torus diffeomorphisms;    loop Lie algebra;    Lie-Poisson structure;   

DOI  :  10.3390/sym12050697

来源: DOAJ

【 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.

【 授权许可】

Unknown