Publication: The Darboux system: finite-rank constraints and Darboux
transformations
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1997-11
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American Institute of Physics
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Abstract
The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, which can be understood as a vectorial Darboux transformation of the exponential background. The method is extended further to obtain vectorial Darboux transformations of the Darboux system.
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1.G. Darboux, Lec¸ons sur la Theórie Générale des Surfaces IV, Liv. VIII (Gauthier-Villars, Paris, 1896), Chap. XII.
2.L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces (Ginn, Boston, 1909); An Introduction to Differential Geometry with use of Tensor Analysis (Princeton U. P., Princeton, NJ, 1940).
3.A. R. Forsyth, Lectures on the Differential Geometry of Curves and Surfaces (Cambridge U.P., Cambridge, 1912).
4.V. E. Zakharov and S. E. Manakov, Funct. Anal. Appl. 19, 89 (1985).
5.M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Math. Soc. Lec. Not. Ser. 149 (Cambridge U.P., Cambridge, 1989).
6.V. E. Zakharov, Sov. Phys. Dokl. 21, 322 (1976).
7.V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl. 8, 226 (1974).
8. H. Cornille, J. Math. Phys. 20, 1653 (1979).
9.M. J. Ablowitz and R. Haberman, Phys. Rev. Lett. 35, 1185 (1975).
10.D. J. Kaup, Physica D 1, 45 (1981); 3, 374 (1981); J. Math. Phys. 22, 1176 (1981).
11. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
12.B. Coppi, M. N. Rosenbluth, and R. N. Sudan, Ann. Phys. 55, 207 (1969).
13.V. E. Zakharov, S. L. Musher, and A. M. Rubenckik, Phys. Rep. 129, 285 (1986).
14.D. J. Kaup, A. Reiman, and A. Bers, Rev. Mod. Phys. 51, 275 (1979).
15.F. Guil, M. Mañas, and G. Álvarez, Phys. Lett. A 190, 49 (1994).
16.F. Guil and M. Mañas, J. Phys. A 28, 1713 (1995).
17.F. Guil and M. Mañas, Phys. Lett. A 209, 29 (1995).
18.F. Guil and M. Mañas, J. Phys. A 29, 641 (1996).
19.F. Guil and M. Mañas, Phys. Lett. A 217, 1 (1996).
20.M. Mañas, J. Phys. A 29, 7721 (1996).
21.M. Mañas, A. Doliwa, and P. M. Santini, Phys. Lett. A 233, 365 (1997).
22.Q. P. Liu and M. Mañas, Phys. Lett. B 394, 337 (1997).
23.M. Mañas and P. M. Santini, Phys. Lett. A 227, 325 (1997).
24.Th. F. Moutard, C. R. Acad. Sci. Paris 80, 729 (1875); J. l’Ecole Polytech. 45, 1 (1878).
25.G. Darboux, C. R. Acad. Sci. Paris 94, 1456 (1882); 94, 120, 158, 1290 (1882).
26.V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1990).