Bispectral Darboux transformations: The generalized Airy case

Physica D: Nonlinear Phenomena

Volumn 102, Issue 3-4, 1997, Pages 159-176

  Kasman, Alex ^a,b   Rothstein, Mitchell ^a  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001009854     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00208-4     Document Type: Article

References (20)

1. 1+∞, Darboux transformations and the bispectral problem, q-alg/9601017.
2. J.L. Burchnall and T.W. Chaundy, Commutative ordinary differential operators, Proc. London Math. Soc. 211 (1923) 420-440;
3. Commutative ordinary differential operators, Proc. Roy. Soc. A 118 (1928) 557-583.
4. J.J. Duistermaat and F.A. Grünbaum, Differential equations in the spectral parameter, Comm. Math. Phys. 103 (1986) 177-240.
5. F.A. Grünbaum, The limited angle problem in tomography and some related mathematical problems, in: Bifurcation Theory, Mechanics and Physics (Reidel, Dordrecht, 1983) pp. 317-329.
6. F.A. Grünbaum, The Kadomtsev-Petviashvili equation: An alternative approach to the 'rank two' solutions of Krichever and Novikov, Phys. Lett. A 139 (1989) 146-150.
7. F.A. Grünbaum, Time-band limiting and the bispectral problem, Comm. Pure Appl. Math. 157 (1994) 307-328.
8. A. Kasman, Bispectral KP solutions and linearization of Calogero-Moser particle systems, Comm. Math. Phys. 172 (1995) 427-448
9. A. Kasman, Darboux transformations from n-KdV to KP, in preparation; Rank r KP solutions with singular rational spectral curves, Ph.D. Thesis, Boston University (1995).
10. G. Latham and E. Previato, Higher rank Darboux transformations, MSRI preprint 05229-91; Proc. NATO ARW Nonsingular Limits of Dispersive Waves (Plenum Press, New York, to appear).
11. V.B. Matveev, Darboux transformation and explicit solutions of the Kadomtcev-Petviaschvily equation, depending on functional parameters, Lett. Math. Phys. 3 (1979) 213-216.
12. E. Previato, Seventy years of spectral curves: 1923-1993, in: Proc. CIME 1993, Lecture Notes in Physics (Springer, Berlin, to appear).
13. E. Previato and G. Wilson, Vector bundles over curves and solutions of the KP equations, Proc. Sympos. Pure Math. 49 (1989) 553-569.
14. G. Segal and G. Wilson, Loop groups and equations of KdV type Publications Mathematiques No. 61 de l'Institut des Hautes Etudes Scientifiques (1985) pp. 5-65.
15. A.P. Veselov, Rational solutions of the KP equation and Hamiltonian systems, Comm. Moscow Math. Soc., Russian Math. Surveys 35 (1) (1980) 239-240.
16. G. Wilson, Bispectral commutative ordinary differential operators, J. Reine Angew. Math. 442 (1993) 177-204.
17. P. Wright, Darboux transformations, algebraic subvarieties of Grassmann manifolds, commuting flows and bispectrality, Ph.D. Thesis, Berkeley (1987).
18. J. Zubelli, Differential equations in the spectral parameter for matrix differential operators, Physica D 43 (1990) 269-287.
19. J. Zubelli, On the polynomial tau function for the KP hierarchy and the bispectral property, Lett. Math. Phys. 24 (1992) 41-48.
20. J. Zubelli and F. Magri, Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV, Comm. Math. Phys. 141 (1991) 329-351.