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arXiv · 1205.3415

On The Complete Integrability Of The Ostrovsky-Vakhnenko Equation

Yarema A. Prykarpatsky
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Abstract

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.

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Yarema A. Prykarpatsky. 2012-05-12. On The Complete Integrability Of The Ostrovsky-Vakhnenko Equation. https://arxiv.org/abs/1205.3415

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