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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

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.

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

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.