The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated W algebra

Communications in Mathematical Physics

Volumn 175, Issue 1, 1996, Pages 177-202

  Bonora, L ^a,b   Liu, Q P ^c   Xiong, C S ^d  

^a SISSA   (Italy)

^b SEZIONE DI TRIESTE   (Italy)

^c INSTITUTE OF THEORETICAL PHYSICS   (China)

^d UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030540080     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02101629     Document Type: Article

References (37)

1. Dickey, L.: Soliton equations and Hamiltonian systems. Singapore: World Scientific, 1991; Babelon, O., Viallet, C.: Lecture notes in SISSA (1989); Das, A.: Integrable Models. Singapore: World Scientific, 1988
2. Dickey, L.: Soliton equations and Hamiltonian systems. Singapore: World Scientific, 1991; Babelon, O., Viallet, C.: Lecture notes in SISSA (1989); Das, A.: Integrable Models. Singapore: World Scientific, 1988
3. Dickey, L.: Soliton equations and Hamiltonian systems. Singapore: World Scientific, 1991; Babelon, O., Viallet, C.: Lecture notes in SISSA (1989); Das, A.: Integrable Models. Singapore: World Scientific, 1988
4. Drinfeld, V.G., Sokolov, V.V.: J. Sov. Math. 30, 1975 (1984)
5. de Groot, M., Hollowood, T., Miramontes, J.: Commun. Math. Phys. 145, 57 (1992)
6. Fehér, L., Harnad, J., Marshall, I.: Commun. Math. Phys. 154, 181 (1993)
7. Fernàndez-Pousa, C.R., Gallas, M.V., Miramontes, J.L., Guillèn, J.S.: W-Algebras from Heisenberg subalgebras. US-FT/13-94, hep-th/9409016
8. See, for example, Ueno, K., Takasaki, K.: Adv. Stu. Pure Math. 4, 1 (1984)
9. th KdV hierarchy and the associated W algebras. SISSA 171/93/EP, BONN-HE/45/93, to be published in J. Math. Phys.
10. Bonora, L., Xiong, C.S.: Phys. Lett. B285, 191 (1992), Nucl. Phys. B405 (1993)
11. Bonora, L., Xiong, C.S.: Phys. Lett. B285, 191 (1992), Nucl. Phys. B405 (1993)
12. Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Phys. Lett. B316, 85 (1993); Aratyn, H., Nissimov, E., Pacheva, S., Zimerman, A.H.: Two-matrix string model as constrained (2 + 1)-Dimensional integrable system, hepth/9407017
13. Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Phys. Lett. B316, 85 (1993); Aratyn, H., Nissimov, E., Pacheva, S., Zimerman, A.H.: Two-matrix string model as constrained (2 + 1)-Dimensional integrable system, hepth/9407017
14. Di Francesco, P., Itzykson, C., Zuber, J.-B.: Commun. Math. Phys. 140, 543 (1991); Huang, W.J.: J. Math. Phys. 35, 993 (1994)
15. Di Francesco, P., Itzykson, C., Zuber, J.-B.: Commun. Math. Phys. 140, 543 (1991); Huang, W.J.: J. Math. Phys. 35, 993 (1994)
16. Mathieu, P.: Phys. Lett. B208, 101 (1988)
17. Balog, J., Fehér, L., O'Raifeartaigh, L., Forgacs, P., Wipf, A.: Ann. Phys. 203, 76 (1990); Fehér L., O'Raifeartaigh, L., Ruelle, P., Tsutsui, I., Wipf, A.: Phys. Rep. 222, 1 (1992); Bouwknegt, P., Schoutens, K.: Phys. Rep. 223, 183 (1993)
18. Balog, J., Fehér, L., O'Raifeartaigh, L., Forgacs, P., Wipf, A.: Ann. Phys. 203, 76 (1990); Fehér L., O'Raifeartaigh, L., Ruelle, P., Tsutsui, I., Wipf, A.: Phys. Rep. 222, 1 (1992); Bouwknegt, P., Schoutens, K.: Phys. Rep. 223, 183 (1993)
19. Balog, J., Fehér, L., O'Raifeartaigh, L., Forgacs, P., Wipf, A.: Ann. Phys. 203, 76 (1990); Fehér L., O'Raifeartaigh, L., Ruelle, P., Tsutsui, I., Wipf, A.: Phys. Rep. 222, 1 (1992); Bouwknegt, P., Schoutens, K.: Phys. Rep. 223, 183 (1993)
20. Polyakov, A.: Int. J. Mod. Phys. A5, 85 (1990)
21. Watanabe, Y.: Lett. Math. Phys. 7, 99 (1983); Dickey, L.A.: Ann. N.Y. Acad. Sci. 491, 131 (1987);
22. Watanabe, Y.: Lett. Math. Phys. 7, 99 (1983); Dickey, L.A.: Ann. N.Y. Acad. Sci. 491, 131 (1987);
23. Radul, A.O.: In: Applied methods of nonlinear analysis and control. Mironov et al. (ed.) MGU, (1987) p. 149 (in Russian)
24. Cheng, Y.: J. Math. Phys. 33, 3774 (1992)
25. Wu, Y.-S. and Yu, F.: Phys. Rev. Lett. 66, 2996 (1992); Depireux, D.: Mod. Phys. Lett. A7, 1825 (1992); Depireux, D., Schiff, J.: On the Hamiltonian structures and the reductions of KP hierarchy. Preprint, IASSNS-HEP-92-66; Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Nucl. Phys. B402, 85 (1993)
26. Wu, Y.-S. and Yu, F.: Phys. Rev. Lett. 66, 2996 (1992); Depireux, D.: Mod. Phys. Lett. A7, 1825 (1992); Depireux, D., Schiff, J.: On the Hamiltonian structures and the reductions of KP hierarchy. Preprint, IASSNS-HEP-92-66; Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Nucl. Phys. B402, 85 (1993)
27. Wu, Y.-S. and Yu, F.: Phys. Rev. Lett. 66, 2996 (1992); Depireux, D.: Mod. Phys. Lett. A7, 1825 (1992); Depireux, D., Schiff, J.: On the Hamiltonian structures and the reductions of KP hierarchy. Preprint, IASSNS-HEP-92-66; Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Nucl. Phys. B402, 85 (1993)
28. Wu, Y.-S. and Yu, F.: Phys. Rev. Lett. 66, 2996 (1992); Depireux, D.: Mod. Phys. Lett. A7, 1825 (1992); Depireux, D., Schiff, J.: On the Hamiltonian structures and the reductions of KP hierarchy. Preprint, IASSNS-HEP-92-66; Aratyn, H., Ferreira, L.A., Gomez, J.F., Zimerman, A.H.: Nucl. Phys. B402, 85 (1993)
29. Kupershmidt, B.A.: Commun. Math. Phys. 99, 51 (1985)
30. Brunelli, J.C., Das, A., Huang, W.J.: Gelfand-Dickii brackets for non-standard Lax equations. Rochester print, UR-1347, ER-40685-796, hepth/9405111
31. Liu, Q.P., Xiong, C.S.: Phys. Lett. B327, 329 (1994); Liu, Q.P.: Phys. Lett. A187, 373 (1994)
32. Liu, Q.P., Xiong, C.S.: Phys. Lett. B327, 329 (1994); Liu, Q.P.: Phys. Lett. A187, 373 (1994)
33. Bonora, L., Xiong, C.S.: Phys. Lett. B317, 329 (1994)
34. Delduc, F., Frappat, L., Ragoucy, E., Sorba, P., Toppan, F.: Phys. Lett. B318, 457 (1993); Toppan, F.: Generalized NLS hierarchies from rational W-algebras. hepth/9312045
35. Delduc, F., Frappat, L., Ragoucy, E., Sorba, P., Toppan, F.: Phys. Lett. B318, 457 (1993); Toppan, F.: Generalized NLS hierarchies from rational W-algebras. hepth/9312045
36. Yu, F.: Lett. Math. Phys. 29, 175 (1993)
37. Dickey, L.: On the constrained KP hierarchy. Oklahoma preprint, hepth/9407038