On The Complete Integrability Of The Ostrovsky-Vakhnenko Equation

The complete integrability of the Ostrovsky-Vakhnenko equation is studied by means of symplectic gradient-holonomic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related infinite hierarchies of conservation laws are constructed....

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2012-05
Main Author: Prykarpatsky, Yarema A
Format: Article
Language:English
Subjects:
Conservation laws
Differential equations
Hierarchies
Hydrodynamic equations
Integral equations
Polynomials
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The complete integrability of the Ostrovsky-Vakhnenko equation is studied by means of symplectic gradient-holonomic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related infinite hierarchies of conservation laws are constructed. A new bi-infinite hierarchy of completely Lax type integrable Riemann type hydrodynamical systems is proposed. It is demonstrated that at s=3 the corresponding Riemann type hydrodynamical equation is related with the Degasperis-Processi equation, whose reduction gives rise to the Ostrovsky-Vakhnenko equation.
ISSN:2331-8422