Hamiltonian structures for the Ostrovsky–Vakhnenko equation

Hamiltonian structures for the Ostrovsky–Vakhnenko equation

► A fifth order Ostrovsky–Vakhnenko equation is shown to be related with the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. ► The bi-Hamiltonian formulation for Ostrovsky–Vakhnenko equation is derived. ► The relation between Hamiltonian structures when dependent and independent variables are transforme...

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Veröffentlicht in:Communications in nonlinear science & numerical simulation 2013-01, Vol.18 (1), p.56-62
Hauptverfasser: Brunelli, J.C., Sakovich, S.
Format: Artikel
Sprache:eng
Schlagworte:
Bi-Hamiltonian systems
Computer simulation
Derivation
Independent variables
Integrable models
Mathematical analysis
Mathematical models
Miura-type transformations
Nonlinear evolution equations
Nonlinearity
Symmetry
Transformations
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Zusammenfassung:► A fifth order Ostrovsky–Vakhnenko equation is shown to be related with the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. ► The bi-Hamiltonian formulation for Ostrovsky–Vakhnenko equation is derived. ► The relation between Hamiltonian structures when dependent and independent variables are transformed is studied. We obtain a bi-Hamiltonian formulation for the Ostrovsky–Vakhnenko (OV) equation using its higher order symmetry and a new transformation to the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2012.06.018