Hirota bilinear method for nonlinear evolution equations

  • Junkichi Satsuma
Part of the Lecture Notes in Physics book series (LNP, volume 632)


The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrödinger and Toda equations are given to show how solutions are derived. Then after considering multi-dimensional systems such as the Kadomtsev-Petviashvili, two dimensional Toda and Hirota-Miwa equations, the algebraic structure of such nonlinear evolution systems is explained. Finally, extensions of the method including q-analogue, ultra-discrete systems and trilinear forms are also presented.


Vertex Operator Soliton Solution Nonlinear Evolution Equation Soliton Equation Toda Equation 
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Authors and Affiliations

  • Junkichi Satsuma
    • 1
  1. 1.Graduate School of Mathematical Sciences, The University of Tokyo, 3–8–1 Komaba, Meguro-ku, Tokyo 153–8914Japan

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