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
AbstractA 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.
|Journal series||Reports on Mathematical Physics, ISSN 0034-4877, (A 15 pkt)|
|Publication size in sheets||2.3|
|Keywords in English||differential-algebraic methods, gradient holonomic algorithm, Lax type integrability, compatible Poisson structures, Lax-type representation, generalized Ostrovsky-Vakhnenko equation, Degasperis-Processi equation|
|Score|| = 15.0, 26-07-2017, ArticleFromJournal|
= 20.0, 26-07-2017, ArticleFromJournal
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.