The vector k-constrained KP hierarchy and Sato's Grassmannian

Journal of Geometry and Physics

Volumn 23, Issue 1, 1997, Pages 83-96

  Van De Leur, Johan ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Constrained KP; Infinite Grassmannian; KP hierarchy

Indexed keywords

EID: 0031206162     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(97)81154-0     Document Type: Article

References (28)

1. [AFGZ] H. Aratyn, L. Ferreira, J.F. Gomes and A.H. Zimerman, Constrained KP models as integrable matrix hierarchies, hep-th 9509096.
2. [ANP] H. Aratyn, E. Nissimov and S. Pacheva, Constrained KP hierarchies: Additional symmetries, Darboux-Bäcklund solutions and relations to multi-matrix models, hep-th 9607234.
3. [C] Yi Cheng, Modifying the KP, the nth constrained KP hierarchies and their hamiltonian structures, Commun. Math. Phys. 171 (1995) 661-682.
4. [CSZ] Yi Cheng, W. Strampp and B. Zhang, Constraints of the KP hierarchy and multilinear forms, Commun. Math. Phys. 168 (1995) 117-135.
5. [CZ] Yi Cheng, Y.-J. Zhang, Bilinear equations for the constrained KP hierarchy, Inverse Problems 10 (1994) L11-L17.
6. [DJKM1] E. Date, M. Jimbo, M. Kashiwara and T. Miwa, Operator approach to the Kadomtsev-Petviashvili equation. Transformation groups for soliton equations. III, J. Phys. Soc. Japan 50 (1981) 3806-3812.
7. [DJKM2] E. Date, M. Jimbo, M. Kashiwara and T. Miwa, Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy, Publ. Res. Inst. Math. Sci. 18 (1982) 1077-1110.
8. [DJKM3] E. Date, M. Jimbo, M. Kashiwara and T. Miwa, Transformation groups for soliton equations, in: Nonlinear Integrable systems-Classical Theory and Quantum Theory, eds. M. Jimbo and T. Miwa (World Scientific, Singapore, 1983) pp. 39-120.
9. [D] L.A. Dickey, and On the constrained KP, preprint.
10. [DS] L. Dickey and W. Strampp, On new identities for KP Baker functions and their application to constrained hierarchies, preprint.
11. [FK] I.B. Frenkel and V.G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980) 23-66.
12. [HV] G.F. Helminck and J.W. van de Leur, An analytic description of the vector constrained KP hierarchy, in preparation.
13. [JM] M. Jimbo and T. Miwa, Solitons and infinite dimensional Lie algebras, Publ. Res. Inst. Math. Sci. 19 (1983) 943-1001.
14. [K] I. Krichever, General rational reductions of the KP hierarchy and their symmetries, preprint.
15. [KP1] V.G. Kac and D.H. Peterson, Spin and wedge representations of infinite-dimensional Lie algebras and groups, Proc. Nat. Acad. Sci. USA 78 (1981) 3308-3312.
16. [KP2] V.G. Kac and D.H. Peterson, Lectures on the infinite wedge representation and the MKP hierarchy, Séminaire de Mathematiques Supérieures, Vol. 102 (Presses University Montreal, Montreal, 1986) pp.141-184.
17. [KR] V.G. Kac and A.K. Raina, Bombay lectures on highest weight representations of infinite-dimensional Lie algebras, Advanced Series in Mathematical Physics, Vol. 2 (World Scientific, Singapore, 1987).
18. [KV] V.G. Kac and J.W. van de Leur, The n-component KP hierarchy and representation theory, in: Important Developments in Soliton Theory, eds. A.S. Fokas and V.E. Zakharov, Springer Series in Nonlinear Dynamics (Springer, Berlin, 1993) pp.302-343.
19. [LW] I. Loris and R. Willox, Bilinear form and solutions of the k-constrained Kadomtsev-Petviashvili hierarchy, preprint.
20. [M] M. Mulase, Algebraic theory of the KP equations, in: Perspectives in Mathematical Physics, eds. R. Penner and S.-T. Yau (International Press Company, 1994) pp.157-223.
21. [OS] W. Oevel and W. Strampp, Constrained KP hierarchies and bi-hamiltonian structures, Commun. Math. Phys. 157 (1993) 51-81.
22. [S] M. Sato, Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds, Res. Inst. Math. Sci. Kokyuroku 439 (1981) 30-46.
23. [SS] J. Sidorenko and W. Strampp, Multicomponent integrable reductions in the Kadomtsev-Petviashvilli hierarchy, J. Math. Phys. 34 (1993) 1429-1446.
24. [SW] G. Segal and G. Wilson, Loop groups and equations of KdV type, Inst. Hautes Etudes Sci. Publ. Math. 63 (1985) 1-64.
25. n, Commun. Math. Phys. 137 (1991) 67-107.
26. [V] J. van de Leur, A geometrical interpretation of the constrained KP hierarchy, preprint.
27. [Z] Y.-Z. Zhang, On Segal-Wilson's construction for the τ-function of the constrained KP hierarchies, Lett. Math. Phys. 36 (1996) 1-15.
28. [ZC] Y.-J. Zhang and Yi Cheng, Solutions for the vector k-constrained KP hierarchy, J. Math. Phys. 35 (1994) 5869-5884.