The AKNS hierarchy and the Gurevich-Zybin dynamical system integrability revisited

Анотація

A novel approach based upon vertex operator representation is devised to study the AKNS hierarchy. It is shown that this method reveals there markable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed. 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 Hamiltonian flows is obtained.