Deformations of the KdV Hierarchy and Related Soliton Equations

International Mathematics Research Notices

Volumn , Issue 2, 1996, Pages 54-76

  Frenkel, Edward ^a  

^a HARVARD UNIVERSITY   (United States)

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EID: 1842453908     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. M. Adler, On a trace functional for formal pseudodifferential operators and the symplectic structure of the Korteweg-de Vries type equations, Invent. Math. 50 (1979), 219-248.
2. N algebras and Macdonald polynomials, preprint q-alg/9508011.
3. I. Cherednik, Differential equations for the Baker-Akhiezer functions of algebraic curves, Functional Anal. Appl. 12 (1978), 195-203.
4. L. A. Dickey, Soliton Equations and Hamiltonian Systems, Adv. Ser. Math. Phys. 12, World Scientific, River Edge, N.J., 1991.
5. V. G. Drinfeld and V. V. Sokolov, Equations of Korteweg-de Vries type and simple Lie algebras, Dokl. Akad. Nauk. SSSR 258 (1981), 11-16 (in Russian); Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30 (1985), 1975-2035.
6. V. G. Drinfeld and V. V. Sokolov, Equations of Korteweg-de Vries type and simple Lie algebras, Dokl. Akad. Nauk. SSSR 258 (1981), 11-16 (in Russian); Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30 (1985), 1975-2035.
7. T. Eguchi and S.-K. Yang, Deformations of conformal field theories and soliton equations, Phys. Lett. B 224 (1989), 373-378.
8. V. Fateev and S. Lukyanov, Additional symmetries and exactly soluble models in two-dimensional conformal field theory, Kiev Preprints ITF-88-74R, ITF-88-75R, ITF-88-76R, 1988, English translation in Soviet Sci. Rev. A Phys. 15 (1990).
9. V. Fateev and S. Lukyanov, Additional symmetries and exactly soluble models in two-dimensional conformal field theory, Kiev Preprints ITF-88-74R, ITF-88-75R, ITF-88-76R, 1988, English translation in Soviet Sci. Rev. A Phys. 15 (1990).
10. B. Feigin and E. Frenkel, Free field resolutions in affine Toda field theories, Phys. Lett. 276 (1992), 79-86.
11. _, Integrals of motion and quantum groups, preprint hep-th/9310022, to appear in Lecture Notes in Math. 1620, Springer-Verlag, New York, 1995.
12. _, Kac-Moody groups and integrability of soliton equations, Invent. Math. 120 (1995), 379-408.
13. _, Quantum W-algebras and elliptic algebras, preprint q-alg/9508009.
14. B. Feigin, E. Frenkel, and A. Odesskii, Commutative subalgebras of the quantum Virasoro algebra, in preparation.
15. H. Flaschka, Construction of conservation laws for Lax equations, Quart. J. Math. Oxford Ser. (2) 34 (1983), 61-65.
16. E. Frenkel, Deformations of the classical W-algebras and related soliton hierarchies, in preparation.
17. E. Frenkel and N. Reshetikhin, Quantum affine algebras and deformations of the Virasoro and W-algebras, preprint q-alg/9505025, to appear in Comm. Math. Phys.
18. I. M. Gelfand and L. A. Dikki, A family of Hamiltonian structures connected with integrable nonlinear differential equations, Akad. Nauk. SSSR Inst. Prikl. Mat. Preprint 136 (1978); reprinted in W-symmetry, ed. by P. Bouwknegt and K. Schoutens, World Scientific, Singapore, 1995, 3-24.
19. I. M. Gelfand and L. A. Dikki, A family of Hamiltonian structures connected with integrable nonlinear differential equations, Akad. Nauk. SSSR Inst. Prikl. Mat. Preprint 136 (1978); reprinted in W-symmetry, ed. by P. Bouwknegt and K. Schoutens, World Scientific, Singapore, 1995, 3-24.
20. D. Gieseker, The Toda hierarchy and the KdV hierarchy, preprint alg-geom/9509006.
21. B. A. Kupershmidt, Discrete Lax Equations and Differential-Difference Calculus, Astérisque 123 (1985).
22. B. A. Kupershmidt and G. Wilson, Conservation laws and symmetries of generalized sine-Gordon equations, Comm. Math. Phys. 81 (1981), 189-202.
23. _, Modifying Lax equations and the second Hamiltonian structure, Invent. Math. 62 (1981), 403-436.
24. S. Lukyanov and Ya. Pugai, Bosonization of ZF algebras: direction toward deformed Virasoro algebra, preprint hep-th/9412128.
25. F. Magri, A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), 1156-1162.
26. J. Shiraishi, H. Kubo, H. Awata, and S. Odake, A quantum deformation of the Virasoro algebra and Macdonald symmetric functions, preprint q/alg-9507034.
27. V. V. Sokolov and A. B. Shabat, (L, A)-pairs and Ricatti type substitution, Funct. Anal. Appl. 14 (1980), 148-150.
28. G. Wilson, On two constructions of conservation laws for Lax equations, Quart. J. Math. Oxford Ser. (2) 32 (1981), 491-512.
29. A. B. Zamolodchikov, "Integrable field theory from conformal field theory" in Integrable Systems in Quantum Field Theory and Statistical Mechanics, Adv. Stud. Pure Math. 19, Academic Press, Boston, 1989, 641-674.