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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 002, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.002 (Mi sigma459) 		 
This article is cited in 21 scientific papers (total in 21 papers)

On a Nonlocal Ostrovsky–Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

Jołanta Goleniaa, Maxim V. Pavlovb, Ziemowit Popowiczc, Anatoliy K. Prykarpatskyda

a AGH University of Science and Technology
b Department of Mathematical Physics, P. N. Lebedev Physical Institute, 53 Leninskij Prospekt, Moscow 119991, Russia
c The Institute for Theoretical Physics, University of Wrocław, Wrocław 50204, Poland
d Department of Economical Cybernetics, Ivan Franko State Pedagogical University, Drohobych, Lviv Region, Ukraine
Full-text PDF (257 kB) Citations (21)
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DOI: https://doi.org/10.3842/SIGMA.2010.002
Abstract: Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case $N=3$ are constructed.
Keywords: generalized Riemann type hydrodynamical equations; Whitham typedynamical systems; Hamiltonian systems; Lax type integrability;gradient-holonomic algorithm.
Received: October 14, 2009; in final form January 3, 2010; Published online January 7, 2010
Bibliographic databases:
Document Type: Article
MSC: 35C05; 37K10
Language: English
Citation: Jołanta Golenia, Maxim V. Pavlov, Ziemowit Popowicz, Anatoliy K. Prykarpatsky, “On a Nonlocal Ostrovsky–Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability”, SIGMA, 6 (2010), 002, 13 pp.
Citation in format AMSBIB
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\paper On a~Nonlocal Ostrovsky--Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability
\jour SIGMA
\yr 2010
\vol 6
\papernumber 002
\totalpages 13
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    		Symmetry, Integrability and Geometry: Methods and Applications
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