Theoretical and Mathematical Physics

, Volume 103, Issue 1, pp 482–485 | Cite as

On the theory of Laplace-Darboux transformations

  • A. B. Shabat


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.


Linear Equation Darboux Theory 
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    G. Darboux,Théorie Generale des Surfaces, Chelsea, New York (1972).Google Scholar
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    V. É. Adler,Funktsional Analiz i Ego Prilozhen.,27(2), 79 (1993).Google Scholar
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    A. P. Veselov and A. B. Shabat,Funktsional Analiz i Ego Prilozhen.,27(2), 1 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. B. Shabat
    • 1
  1. 1.L. D. Landau Institute of Theoretical PhysicsMoscow

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