Opuscula Math. 33, no. 1 (2013), 139-149
A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation
Yarema A. Prykarpatsky
Denis Blackmore
Jolanta Golenia
Anatoliy K. Prykarpatsky
Abstract.
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.
Keywords:
Lax type integrability, vertex operator representation, Lax integrability, Lie-algebraic approach.
Mathematics Subject Classification:
58A30, 56B05, 34B15.
About the authors ▼
Yarema A. Prykarpatsky
University of Agriculture, Department of Applied Mathematics, Balicka 253c, 30-198 Kraków, Poland; Department of Differential Equations of the Institute Mathematics at NAS, Kyiv, Ukraine
Denis Blackmore
New Jersey Institute of Technology, Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, Newark, NJ 07102, USA
Jolanta Golenia
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
Anatoliy K. Prykarpatsky
AGH University of Science and Technology, Department of Mining Geodesy and Environment Engineering, al. Mickiewicza 30, 30-059 Krakow, Poland
About the article ▼
Received: 2011-12-14.
Revised: 2012-06-17.
Accepted: 2012-07-14.
Cite this article as ▼
Yarema A. Prykarpatsky, Denis Blackmore, Jolanta Golenia, Anatoliy K. Prykarpatsky, A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation, Opuscula Math. 33, no. 1 (2013), 139-149,
http://dx.doi.org/10.7494/OpMath.2013.33.1.139.
Download this article's citation as: