Communications in Mathematical Physics

, Volume 158, Issue 2, pp 289–314 | Cite as

A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1+1 and 2+1 dimensions

  • Mark J. Ablowitz
  • Sarbarish Chakravarty
  • Leon A. Takhtajan


The self-dual Yang-Mills equations play a central role in the study of integrable systems. In this paper we develop a formalism for deriving a four dimensional integrable hierarchy of commuting nonlinear flows containing the self-dual Yang-Mills flow as the first member. We show that upon appropriate reduction and suitable choice of gauge group it produces virtually all well known hierarchies of soliton equations in 1+1 and 2+1 dimensions and can be considered as a “universal” integrable hierarchy. Prototypical examples of reductions to classical soliton equations are presented and related issues such as recursion operators, symmetries, and conservation laws are discussed.


Neural Network Statistical Physic Soliton Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Mark J. Ablowitz
    • 1
  • Sarbarish Chakravarty
    • 1
  • Leon A. Takhtajan
    • 2
  1. 1.Program in Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of MathematicsState University of New York at Stony BrookStony BrookUSA

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