• Speaker: Ekaterina Shemyakova, Western University (Canada) and Russian Academy of Sciences (Moscow)
  • Title: The Method of Darboux Transformations for Partial Differential operators
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Tue, 28th Feb 2012
  • Abstract:

    Integrability theory is the area of mathematics in which methods are developed for the exact solution of partial differential equations, as well as for the study of their properties. We concentrate on PDEs appearing in Physics and other applications. Darboux transformations constitute one of the important methods used in integrability theory and, as well as being a method for the exact solution of linear PDEs, they are an essential part of the method of Lax pairs, used for the solution of non-linear PDEs. A large series of Darboux transformations may be constructed using Wronskians built from some number of individual solutions of the original PDE. In this talk we prove a long-standing conjecture that this construction captures all possible Darboux transformations for transformations of order two, while for transformations of order one the construction captures everything but two Laplace transformations. An introduction into the theory will be provided.

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