The bi-Hamiltonian theory of the Harry Dym equation

Theoretical and Mathematical Physics

Volumn 133, Issue 2, 2002, Pages 1585-1597

  Pedroni, M ^a   Sciacca, V ^b   Zubelli, J P ^c  

^a UNIVERSITY OF GENOA   (Italy)

^b UNIVERSITY OF PALERMO   (Italy)

^c IMPA   (Brazil)

Author keywords

Bi Hamiltonian formalism; Completely integrable systems; Harry Dym equation

Indexed keywords

EID: 0036441466     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021111213874     Document Type: Conference Paper

References (26)

1. M. Kruskal, "Nonlinear wave equations," in: Dynamical Systems, Theory and Applications (Lect. Notes Phys., Vol. 38, J. Moser, ed.), Springer, Berlin (1975), pp. 310-354.
2. P. C. Sabatier, Lett. Nuovo Cimento (2), 26(15), 483-486 (1979); 26(15), 477-482 (1979); P. C. Sabatier, "Around the classical string problem, " in: Nonlinear Evolution Equations and Dynamical Systems (Lect. Notes Phys., Vol. 120, M. Boiti et al., eds.), Springer, Berlin (1980), pp. 85-102.
3. P. C. Sabatier, Lett. Nuovo Cimento (2), 26(15), 483-486 (1979); 26(15), 477-482 (1979); P. C. Sabatier, "Around the classical string problem, " in: Nonlinear Evolution Equations and Dynamical Systems (Lect. Notes Phys., Vol. 120, M. Boiti et al., eds.), Springer, Berlin (1980), pp. 85-102.
4. P. C. Sabatier, Lett. Nuovo Cimento (2), 26(15), 483-486 (1979); 26(15), 477-482 (1979); P. C. Sabatier, "Around the classical string problem, " in: Nonlinear Evolution Equations and Dynamical Systems (Lect. Notes Phys., Vol. 120, M. Boiti et al., eds.), Springer, Berlin (1980), pp. 85-102.
5. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
6. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
7. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
8. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
9. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
10. C. Rogers, Phys. Lett. A, 120, 15-18 (1987); Ben Yu Guo and C. Rogers, Sci. China Ser. A, 32, 283-295 (1989); V. G. Dubrovsky and B. G. Konopelchenko, J. Phys. A, 27(13), 4619-4628 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Theor. Math. Phys., 99, 337-444 (1994); O. Ragnisco and S. Rauch-Wojciechowski, J. Math. Phys., 35, 834-847 (1994); B. G. Konopelchenko and Jyh-Hao Lee, Phys. D, 81, 32-43 (1995).
11. W. Oevel and S. Carillo, J. Math. Anal. Appl., 217, 161-178, 179-199 (1998).
12. P. Casati, G. Falqui, F. Magri, and M. Pedroni, J. Math. Phys., 38, 4606-4628 (1997).
13. G. Falqui, F. Magri, and M. Pedroni, Comm. Math. Phys., 197, 303-324 (1998).
14. P. Casati, G. Falqui, F. Magri, and M. Pedroni, J. Geom. Phys., 26, 291-310 (1998).
15. F. Magri, M. Pedroni, and J. P. Zubelli, Comm. Math. Phys., 188, 305-325 (1997).
16. G. Falqui, F. Magri, M. Pedroni, and J. P. Zubelli, Theor. Math. Phys., 122, 17-28 (2000).
17. P. Casati, G. Falqui, F. Magri, and M. Pedroni, Lett. Math. Phys., 41, 291-305 (1997).
18. G. Falqui, M. Pedroni, F. Magri, and P. Casati, "Soliton equations, bi-Hamiltonian manifolds, and integrability," Preprint, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro (1997).
19. P. Casati, G. Falqui, F. Magri, M. Pedroni, and J. P. Zubelli, Contemp. Math., 15, 45-65 (1998).
20. F. Magri and M. Pedroni, "KdV equations, KP equations, and bi-Hamiltonian manifolds," in: Proc. 8th Intl. Conf. on Waves and Stability in Continuous Media, Palermo, Italy, October 9-14, 1995: Part 1 (Suppl. Rend. Circ. Mat. Palermo. II, Ser. 45, A. M. Greco et al., eds.), Circolo Matematico di Palermo, Palermo (1996), pp. 377-392.
21. G. Falqui, F. Magri, and M. Pedroni, J. Nonlinear Math. Phys., 8 Suppl., 118-127 (2001).
22. R. M. Miura, C. S. Gardner, and M. D. Kruskal, J. Math. Phys., 9, 1204-1209 (1968).
23. F. Magri, "A geometrical approach to the nonlinear solvable equations.," in: Nonlinear Evolution Equations and Dynamical systems (Lect. Notes Phys., Vol. 120, M. Boiti et al., eds.), Springer, Berlin (1980), pp. 233-263; I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, UK (1993).
24. F. Magri, "A geometrical approach to the nonlinear solvable equations.," in: Nonlinear Evolution Equations and Dynamical systems (Lect. Notes Phys., Vol. 120, M. Boiti et al., eds.), Springer, Berlin (1980), pp. 233-263; I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, UK (1993).
25. L. A. Dickey, Soliton Equations and Hamiltonian Systems, World Scientific, River Edge, N. J. (1991).
26. P. Casati, B. Konopelchenko, and M. Pedroni, Contemp. Math., 18, 59-75 (2000).