2012/05/12 by Yarema A. Prykarpatsky, Prykarpatsky, Yarema A.
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.48550/arxiv.1205.3415
8 pages
openalex publication_date 2012/05/12 · arxiv created 2012/05/22 · arxiv updated 2012/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.