Abstract
We present a method for deriving recursion operators and canonical Lax pairs directly from bilinear identities of the KP type. Examples include the KdV equation, the Boussinesq equation, and a real equivalent of the nonlinear Schrödinger equation.
Similar content being viewed by others
REFERENCES
D. J. Korteweg and G. de Vries, Philos. Mag. Ser. 5, 39, 422–443 (1895).
J. Boussinesq, C. R. Acad. Sci. Paris, 72, 755–759 (1871).
M. Remoissenet, Waves Called Solitons: Concepts and Experiments, Springer, Berlin (1994).
P. J. Olver, Application of Lie Groups to Differential Equations (Grad. Texts Math., Vol. 107), Springer, Berlin (1986).
R. Hirota, “Direct methods in soliton theory,” in: Solitons (R. K. Bullough and P. J Caudrey, eds.), Springer, Berlin (1980), pp. 157–176.
B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl., 15, 539–541 (1970).
R. Willox, “On a direct bilinear operator method in soliton theory,” Ph.D. thesis, Vrije Universiteit Brussel, Brussels (1993).
E. Date, M. Kashiwara, M. Jimbo, and T. Miwa, “Transformation groups for soliton equations,” in: Proc. RIMS Symposium on Non-Linear Integrable Systems: Classical Theory and Quantum Theory (M. Jimbo and T. Miwa, eds.), World Scientific, Singapore (1983), pp. 39–119.
A. S. Fokas and P. M. Santini, Comm. Math. Phys., 116, 449–474 (1988).
B. Fuchssteiner, Nonlinear Anal. Theor. Meth. Appl., 6, 849–862 (1979).
F. Lambert, I. Loris, J. Springael, and R. Willox, J. Phys. A, 27, 5325–5334 (1994); I. Loris and R. Willox, Inverse Problems, 13, 411–420 (1997); I. Loris and R. Willox, J. Phys. A, 30, 6925–6938 (1997).
I. Loris, “Symmetry reductions in the tau-function approach to integrability,” Ph.D. thesis, Vrije Universiteit Brussel, Brussels (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Loris, I. Bilinear Representations of Integrable Equations. Theoretical and Mathematical Physics 133, 1549–1556 (2002). https://doi.org/10.1023/A:1021103012057
Issue Date:
DOI: https://doi.org/10.1023/A:1021103012057