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Open AccessArticle

On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

Department of Applied Mathematics, University of Agriculture in Krakow, 30-059 Krakow, Poland
Symmetry 2020, 12(5), 697; https://doi.org/10.3390/sym12050697
Received: 6 February 2020 / Revised: 26 March 2020 / Accepted: 28 March 2020 / Published: 1 May 2020
(This article belongs to the Special Issue Nonlinear Oscillations and Boundary Value Problems)
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. View Full-Text
Keywords: Lax-Sato compatibility equations; Chaplygin type hydrodynamical equations; Casimir invariants; torus diffeomorphisms; loop Lie algebra; Lie-Poisson structure Lax-Sato compatibility equations; Chaplygin type hydrodynamical equations; Casimir invariants; torus diffeomorphisms; loop Lie algebra; Lie-Poisson structure
MDPI and ACS Style

Prykarpatskyy, Y. On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure. Symmetry 2020, 12, 697.

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