Opuscula Math. 33, no. 1 (), 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

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.