Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{GolPavPop10}
\by Jo\l anta Golenia, Maxim V.~Pavlov, Ziemowit Popowicz, Anatoliy K.~Prykarpatsky
\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
\mathnet{http://mi.mathnet.ru/sigma459}
\crossref{https://doi.org/10.3842/SIGMA.2010.002}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2593380}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000273562500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896059947}
Linking options:
  • https://www.mathnet.ru/eng/sigma459
  • https://www.mathnet.ru/eng/sigma/v6/p2
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:441
    Full-text PDF :93
    References:76
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024