Hamiltonian structures for the Ostrovsky-Vakhnenko equation

DOI10.1016/j.cnsns.2012.06.018zbMath1257.35160arXiv1202.5129OpenAlexW2023174615MaRDI QIDQ695174

J. C. Brunelli, Sergei Sakovich

Publication date: 20 December 2012

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5129

zbMATH Keywords

integrable modelsnonlinear evolution equationsbi-Hamiltonian systemsMiura-type transformations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (17)

Reciprocal link for a coupled Camassa-Holm type equation ⋮ Orbital stability of periodic waves in the class of reduced Ostrovsky equations ⋮ The initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line ⋮ The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamic systems ⋮ New interaction solutions for a (2 + 1)-dimensional Vakhnenko equation ⋮ Global existence of small-norm solutions in the reduced Ostrovsky equation ⋮ Multisoliton solutions of the Degasperis-Procesi equation and its shortwave limit: Darboux transformation approach ⋮ Transformation and integrability of a generalized short pulse equation ⋮ A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue ⋮ The Ostrovsky-Vakhnenko equation: A Riemann-Hilbert approach ⋮ Linear Instability and Uniqueness of the Peaked Periodic Wave in the Reduced Ostrovsky Equation ⋮ A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain ⋮ On spatial discretization of evolutionary differential equations on the periodic domain with a mixed derivative ⋮ A new Liouville transformation for the Geng-Xue system ⋮ A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions ⋮ Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux ⋮ Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation

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