The nxn KdV flows

Details The nxn KdV flows The nxn KdV flows

2006-11-03

arxiv.org/abs/nlin/0611006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

32 pages

Scientific paper

We introduce a new integrable system hierarchy which is a restriction of the AKNS nxn hierarchy coming from an unusual splitting of the loop algebra. This splitting comes from an automorphism of the loop algebra instead of an automorphism of SL(n,C). It is known that the 2x2 KdV is the standard KdV hierarchy. We construct a gauge equivalence of this nxn KdV hierarchy with the Gelfand-Dickey hierarchy. We show that the tau function of Wilson has many of the same properties of the usual tau function.

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