Applications to solutions of differential equations

  • David Mumford
Part of the Modern Birkhäuser Classics book series (MBC)


The corollaries of Fay’s trisecant identity can be used to construct special solutions to many equations occurring in Mathematical Physics. In this section we will consider the following equations:
  1. 1)

    Sine-Gordan: utt − uxx = sin u.

  2. 2)

    Korteweg-de Vries(K-dV): ut + uxxx + u•ux = 0.

  3. 3)

    Kadomtsev-Petviashvili (K-P) ; uyy + (ut+uxxx+u•ux)x = 0.



Differential Equation Mathematical Physic Branch Point Algebraic Geometry Theta Function 


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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • David Mumford
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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