The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems
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. Popow...
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| Veröffentlicht in: | Reports on mathematical physics 2013-06, Vol.71 (3), p.305-351 |
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| container_title | Reports on mathematical physics |
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| creator | Prykarpatsky, Yarema A. Artemovych, Orest D. Pavlov, Maxim V. Prykarpatski, Anatolij K. |
| description | 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. |
| doi_str_mv | 10.1016/S0034-4877(13)60035-X |
| format | Article |
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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. 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| ispartof | Reports on mathematical physics, 2013-06, Vol.71 (3), p.305-351 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Compatibility compatible Poisson structures Computational fluid dynamics Degasperis–Processi equation differential-algebraic methods Fluid flow generalized Ostrovsky–Vakhnenko equation gradient holonomic algorithm Hierarchies Hydrodynamics Integral calculus Lax type integrability Lax-type representation Mathematical analysis Representations |
| title | The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems |
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