Special Solutions of Discrete Integrable Systems

Part of the Lecture Notes in Physics book series (LNP, volume 644)


Hierarchies of discrete soliton equations are constructed in bilinear form as a consequence of the algebraic identities satisfied by determinants and Pfaffians. Difference formulas for determinants and Pfaffians are derived from the discrete linear dispersion relations satisfied by their elements. For completeness, we first summarize the main algebraic properties of determinants and Pfaffians.


Bilinear Form Special Solution Darboux Transformation Soliton Equation Expansion Formula 
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Authors and Affiliations

  • Y. Ohta
    • 1
  1. 1.Department of Mathematics, Kobe University, Rokko, Kobe 657-8501Japan

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