On the constrained KP hierarchy II
- 46 Downloads
A constrained KP hierarchy is discussed that was recently suggested by Aratynet al. and by Bonoraet al. This hierarchy is a restriction of the KP to a submanifold of operators which can be represented as a ratio of two purely differential operators of prescribed orders. Explicit formulas for action of vector fields on these two differential operators are written which gives a new description of the hierarchy and provides a new, more constructive proof of compatibility of the constraint with the hierarchy. Also, the Poisson structure of the constrained hierarchy is discussed.
Mathematics Subject Classifications (1991)35Q58 58F07
Unable to display preview. Download preview PDF.
- 1.Aratyn, H., Nissimov, E. and Pacheva, S., Construction of KP hierarchies in terms of finite number of fields and their abelianization, Preprint, hep-th 9306035 (1993).Google Scholar
- 2.Bonora, L. and Xiong, C. S., The (N, M)th KdV hierarchy and the associatedW algebra, Preprint SISSA, hep-th 9311070 (1993). Bonora, L., Lin, Q. P., and Xiong, C. S., The integrable hierarchy constructed from a pair of higher KdV hierarchies and its associatedW algebra, Preprint, hep-th 9408035 (1994).Google Scholar
- 3.Dickey, L. A., On the constrained KP hierarchy,Lett. Math. Phys. 34, 379–384 (1995).Google Scholar
- 4.Dickey, L. A.,Integrable Equations and Hamiltonian Systems, Advanced Series inMath. Phys. Vol. 12, World Scientific, Singapore, 1991, p. 310.Google Scholar
- 5.Kupershmidt, B. A.,J. Phys. A: Math. Gen. 22 (1989) L993.Google Scholar