PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 9

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation
Prykarpatsky Y. A., Blackmore D., Golenia J., Prykarpatsky A. K.
Opuscula Mathematica
|
2013
|
Vol. 33, no. 1
139-149
EN
An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type hydrodynamical hierarchy is devised. A functional representation generating an infinite hierarchy of dispersive Lax type integrable flows is obtained.
2
Content available Isospectral integrability analysis of dynamical systems on discrete manifolds
Blackmore D., Prykarpatsky A. K., Prykarpatsky Y. A.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 1
41-66
EN
It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco-Tu and Riemann-Burgers dynamical systems.
3
Content available On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Bogoliubov N. N. (Jr.), Blackmore D. L., Somoylenko V. Hr., Prykarpatsky A. K.
Opuscula Mathematica
|
2007
|
Vol. 27, no. 2
187-195
EN
A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
4
Content available Integrable three-dimensional coupled nonlinear dynamical systems related with centrally extended operator Lie algebras
Hentosh O. Ye., Prykarpatsky A. K.
Opuscula Mathematica
|
2007
|
Vol. 27, no. 2
231-244
EN
A hierarchy of Lax-type flows on a dual space to the centrally extended Lie algebra of integral-differential operators with matrix-valued coefficients is considered. By means of a specially constructed Backlund transforniation the Hamiltonian representations for these flows coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems are obtained. The Hamiltonian description of the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax-type linearizations is analysed.
5
Content available Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part. 1
Pytel-Kudela M., Prykarpatsky A.K.
Opuscula Mathematica
|
2006
|
Vol. 26, no. 1
131-136
EN
The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bilinear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
6
Content available The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal, fiber bundles and some applications. Pt. 1
Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K.
Opuscula Mathematica
|
2005
|
Vol. 25, no. 2
287-298
EN
The canonical reduction method on canonically symplectic manifolds is analized in detail, the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are stated. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented.
7
Content available remote The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Pt. 2
Golenia J., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K.
Opuscula Mathematica
|
2004
|
Vol. 24, no. 1
71-83
EN
The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in soliton theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.
8
Content available remote Quantum mathematics: holonomic computing algorithms and their applications. Pt. 2
Prykarpatsky A.K., Taneri U., Blackmore D.L.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
|
2004
|
T. 8, z. 1
43-65
EN
The article continues a presentation of modern quantum mathematics backgrounds started in [1]. A general approach to quantum holonomic computing based on geometric and Lie-algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bundles it is shown that the associated holonomy groups properly realizing quantum computations can be effectively found concerning their application in diverse practical problems.
PL
Artykuł kontynuuje przedstawienie nowoczesnych podstaw matematyki kwantowej zaczęte w pracy [1]. Zaproponowane ogólne podejście do obliczeń kwantowo-holonomicznych bazowane na geometrycznych i Lie-algebraicznych strukturach na rozmaitościach Grassmanna oraz skojarzonych z nimi potoków typu Laxa. Korzystając z różniczkowo-geometrycznych metod, w tym odwzorowania pędu, rozszerzenia centralnego i teorii koneksji na wiązkach Stiefela pokazano, że skojarzone grupy holonomii, właściwie realizujące obliczenia kwantowe, mogą być efektywnie znalezione stosownie do ich zastosowań do wielu zagadnień praktycznych.
9
Content available remote The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Pt. 1
Prykarpatsky A.K., Samoilenko A.M., Prykarpatsky Y.A.
Opuscula Mathematica
|
2003
|
Vol. 23
71-80
EN
A differential-geometric structure of Delsarte transmutation operators in multidimension is desribed, application to the inverse spectral transform problem is discussed.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.