Hidden hierarchies of KdV type on Birkhoff strata

Journal of Geometry and Physics

Volumn 29, Issue 1-2, 1999, Pages 13-34

  Mañas, Manuel ^a   Alonso, Luis Martínez ^a   Medina, Elena ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Birkhoff strata; Grassmannian; functions

Indexed keywords

EID: 0032623120     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(98)00029-1     Document Type: Article

References (29)

1. M. Sato, RIMS Kokyuroku 439 (1981) 30; The KP hierarchy and infinite-dimensional Grassmann manifolds in: Theta Functions, Bowdoin, 1987, Part 1, Proc. Sympos. Pure Math. vol. 49, part 1, AMS, Providence, 1989, p. 51.
2. M. Sato, RIMS Kokyuroku 439 (1981) 30; The KP hierarchy and infinite-dimensional Grassmann manifolds in: Theta Functions, Bowdoin, 1987, Part 1, Proc. Sympos. Pure Math. vol. 49, part 1, AMS, Providence, 1989, p. 51.
3. G. Segal, G. Wilson, Loop Groups and Equations of KdV Type, Publ. Math. IHES 61 (1985) 5.
4. E. Date, M. Kashiwara, T. Miwa, Transformation groups for soliton equations, in: M. Jimbo, T. Miwa (Eds.), Nonlinear Integrable Systems-classical Theory and Quantum Theory, World Scientific, Singapore, 1983.
5. M. Jimbo, T. Miwa, Solitons and Infinite-dimensional Lie Algebras, Publ. RIMS Kyoto University, 19 (1983) 943.
6. E. Witten, Quantum field theory, Grassmannians and algebraic curves, Comm. Math. Phys. 113 (1988) 529.
7. L. Alvarez-Gaumé, C. Gomez, G. Moore, C. Vafa, Strings in the operator formalism, Nucl. Phys. B 303 (1988) 455.
8. M.R. Douglas, Strings in less than one dimension and the generalized KdV hierarchies, Phys. Lett. B 238 (1990) 176.
9. D.J. Gross, A.A. Migdal, Nonperturbative two-dimensional quantum gravity, Phys. Rev. Lett. 64 (1990) 717.
10. E. Brezin, V Kazakov, Exactly solvable field theories of closed strings, Phys. Lett. B 236 (1990) 144.
11. M. Adler, P. van Moerbeke, Birkhoff strata, Bäcklund transformations and limits of isospectral operators, Adv. Math. 108 (1994) 140.
12. M. Adler, L. Haine, P. van Moerbeke, Limit matrices for the toda flow and periodic flags for loop groups, Math. Ann. 296 (1993) 1.
13. M. Jaulent, Y. Miodek, Nonlinear evolution equations associated with energy dependent Schrödinger potentials, Lett. Math. Phys. 1 (1976) 243.
14. L. Martínez Alonso, Schrödinger spectral problems with energy dependent potentials as sources of nonlinear evolution equations, J. Math. Phys. 21 (1980) 2342.
15. M. Antonowicz, A.P. Fordy, Coupled KdV equations with multi-Hamiltonian structures, Physica D 28 (1987) 345.
16. M. Antonowicz, A.P. Fordy, Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems, Comm. Math. Phys. 124 (1989) 465.
17. M. Antonowicz, A.P. Fordy, Coupled Harry-Dym equations with multi-Hamiltonian structures, J. Phys. A 21 (1988) L269.
18. A.P. Fordy, A.G. Reyman, M.A. Semenov-Tian-Shansky, Classical r-matrices and compatible poisson brackets for coupled KdV systems, Lett. Math. Phys. 17 (1989) 25.
19. A. Pressley, G. Segal, Loop Groups, Oxford University Press, Oxford, 1986.
20. E.M. Chirka, Complex Analytic Sets, Kluwer Academic Publisher, Dordrecht, 1989.
21. M.D. Kruskal, The Korteweg-de Vries equation and related evolution equations, AMS Lectures in Appl. Math. 15 (1974) 61.
22. W.R. Thickstu, A system of particles equivalent to solitons, J. Math. Anal. Appl. 55 (1976) 335.
23. H. Airault, H.P. McKean, J. Moser, Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem, Comm. Pure. Appl. Math. 30 (1977) 95.
24. M. Wadati, Y.H. Ichikawa, T. Shimizu, Cusp soliton of a new integrable evolution equation. Prog. Theor. Phys. 64(1980) 1959.
25. W. Hereman, P.P. Banerjee, M.R. Chatterjee, Derivation and implicit solution of the Harry-Dym equation and its connections with the Korteweg-de Vries equation, J. Phys. A 22 (1989) 249.
26. B.G. Konopelchenko, Inverse spectral transform for the Harry-Dym equation on the complex plane, Physica D 81 (1995) 32.
27. I.M. Gel'fand, L.A. Dikii, Asymptotic behavior of the resolvent of the Sturm-Liouville equation and the algebra of the Korteweg-de Vries equation, Russ. Math. Surv. 30 (1975) 67; Hamiltonian operators and algebraic structures connected to them, Func. Anal. Appl. 13 (1979) 6.
28. I.M. Gel'fand, L.A. Dikii, Asymptotic behavior of the resolvent of the Sturm-Liouville equation and the algebra of the Korteweg-de Vries equation, Russ. Math. Surv. 30 (1975) 67; Hamiltonian operators and algebraic structures connected to them, Func. Anal. Appl. 13 (1979) 6.
29. S. Novikov, The periodic problem for the Korteweg-de Vries equation, Func. Anal. Appl. 8 (1974) 236.