On τ-Functions of Zakharov—Shabat and Other Matrix Hierarchies of Integrable Equations

  • L. A. Dickey
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 26)


Matrix hierarchies are: multi-component KP, general Zakharov—Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral parameter. The notion of a τ-function is introduced here in the most general case along with formulas linking τ-functions with wave Baker functions. The method originally invented by Sato et al. for the KP hierarchy is used. This method goes immediately from definitions and does not require any assumption about the character of a solution, being the most general. Applied to the matrix hierarchies, this involves considerable sophistication. The paper is self-contained and does not expect any special prerequisite from a reader.


Soliton Equation Differential Polynomial Baker Function Bilinear Identity Hierarchy Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • L. A. Dickey
    • 1
  1. 1.University of OklahomaNormanUSA

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