A convergent framework for the multicomponent KP-hierarchy

Helminck, G. F.; Post, G. F.

doi:10.1090/S0002-9947-1991-0986025-5

A convergent framework for the multicomponent KP-hierarchy
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by G. F. Helminck and G. F. Post PDF

Trans. Amer. Math. Soc. 324 (1991), 271-292 Request permission

Abstract:

In this paper we describe how to construct convergent solutions of the multicomponent KP-hierarchy, starting from a certain open subset of the Grassmann manifold of a special kind of Banach space, and derive an expression of its solutions in terms of Fredholm determinants. Further we show that the simplest nonscalar reduction of the present hierarchy leads to the AKNS-hierarchy.

References

H. Flaschka, A. C. Newell, and T. Ratiu, Kac-Moody Lie algebras and soliton equations. II. Lax equations associated with $A_{1}^{(1)}$, Phys. D 9 (1983), no. 3, 300–323. MR 732574, DOI 10.1016/0167-2789(83)90274-9

Convergent solutions of the KP-hierarchy

Graeme Segal and George Wilson, Loop groups and equations of KdV type, Inst. Hautes Études Sci. Publ. Math. 61 (1985), 5–65. MR 783348
Kimio Ueno and Kanehisa Takasaki, Toda lattice hierarchy, Group representations and systems of differential equations (Tokyo, 1982) Adv. Stud. Pure Math., vol. 4, North-Holland, Amsterdam, 1984, pp. 1–95. MR 810623, DOI 10.2969/aspm/00410001
George Wilson, Commuting flows and conservation laws for Lax equations, Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 1, 131–143. MR 530817, DOI 10.1017/S0305004100000700