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On the theory of Laplace-Darboux transformations

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Abstract

In the framework of the classical Laplace—Darboux theory, a formula of linear-fractional transformation of the solutions of a second-order linear equation with two independent variables is established. The one-dimensional reduction of the theory is briefly discussed.

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References

  1. G. Darboux,Théorie Generale des Surfaces, Chelsea, New York (1972).

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  2. V. É. Adler,Funktsional Analiz i Ego Prilozhen.,27(2), 79 (1993).

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  3. A. P. Veselov and A. B. Shabat,Funktsional Analiz i Ego Prilozhen.,27(2), 1 (1993).

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Authors and Affiliations

  1. L. D. Landau Institute of Theoretical Physics, Ul. Kosygin 2, 117940, Moscow

    A. B. Shabat

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  1. A. B. Shabat
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Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 170–175, April, 1995.

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Shabat, A.B. On the theory of Laplace-Darboux transformations. Theor Math Phys 103, 482–485 (1995). https://doi.org/10.1007/BF02069791

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  • DOI: https://doi.org/10.1007/BF02069791

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