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Keywords:
diffiety; Darboux transformation; Monge system
diffiety; Darboux transformation; Monge system
Summary:
Automorphisms of the family of all Sturm-Liouville equations $y^{^{\prime \prime }}=qy$ are investigated. The classical Darboux transformation arises as a particular case of a general result.
References:
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[2] Beals, R., Deift, P., Tomei, C.: Direct and inverse Scattering on the Line. Mathematical Surveys and Monographs 28, AMS 1988, pp. 171–180. MR 0954382
[3] Matveev, V. B., Salle, M. A.: Darboux Transformations and Solitons. Springer Series in Nonlinear Dynamics, Springer Verlag 1991. MR 1146435
[4] Chrastina, J.: On the equivalence of variational problems II. Archivum Mathematicum (Brno) T. 29 (1993), 197–220. MR 1263122 | Zbl 0821.49009
[5] Chrastina, J.: Preprint to the theory of diffieties.
[6] Vinogradov, A. M., Krasilščik, I. S., Lyčagin, V. V.: Introduction into the geometry of nonlinear differential equations. (Russian), Moskva 1986.
[7] Chrastinov , V.: On the Darboux transformation I. Georgian Mathematical Journal Vol. 2, No. 3, 1995, 237–240. MR 1334879
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