RT Journal Article
T1 The Darboux system: finite-rank constraints and Darbouxtransformations
A1 Guil Guerrero, Francisco
A1 Mañas Baena, Manuel
AB 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.
PB American Institute of Physics
SN 0022-2488
YR 1997
FD 1997-11
LK https://hdl.handle.net/20.500.14352/59738
UL https://hdl.handle.net/20.500.14352/59738
LA eng
NO 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).
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