The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamic systems

Yarema A. Prykarpatskyy , Orest D. Artemovych , Maxim V. Pavlov , Anatolij K. Prykarpatsky

Abstract

A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.
Author Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
, Orest D. Artemovych
Orest D. Artemovych,,
-
, Maxim V. Pavlov
Maxim V. Pavlov,,
-
, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
-
Journal seriesReports on Mathematical Physics, ISSN 0034-4877, (A 15 pkt)
Issue year2013
Vol71
No3
Pages305-351
Publication size in sheets2.3
Keywords in Englishdifferential-algebraic methods, gradient holonomic algorithm, Lax type integrability, compatible Poisson structures, Lax-type representation, generalized Ostrovsky-Vakhnenko equation, Degasperis-Processi equation
DOIDOI:10.1016/S0034-4877(13)60035-X
URL http://www.sciencedirect.com/science/article/pii/S003448771360035X
Internal identifierWIŚIG/2013/109
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 15.0, 26-07-2017, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 26-07-2017, ArticleFromJournal
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