Title of article
The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems
Author/Authors
Prykarpatsky، نويسنده , , Yarema A. and Artemovych، نويسنده , , Orest D. and Pavlov، نويسنده , , Maxim V. and Prykarpatski، نويسنده , , Anatolij K. and Soltanov، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2013
Pages
47
From page
305
To page
351
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.
Keywords
differential-algebraic methods , gradient holonomic algorithm , compatible Poisson structures , Lax-type representation , generalized Ostrovsky–Vakhnenko equation , Degasperis–Processi equation , Lax type integrability
Journal title
Reports on Mathematical Physics
Serial Year
2013
Journal title
Reports on Mathematical Physics
Record number
1990561
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