Opuscula Math. 33, no. 1 (2013), 139-149
http://dx.doi.org/10.7494/OpMath.2013.33.1.139
Opuscula Mathematica
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.
- 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
- Received: 2011-12-14.
- Revised: 2012-06-17.
- Accepted: 2012-07-14.
