Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation

  • Bernard Deconinck
  • Harvey Segur


The real, nonsingular elliptic solutions of the Korteweg-de Vries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This constraint is solvable for any finite number of poles located in the fundamental domain of the elliptic function, often in many different ways. Special consideration is given to those elliptic solutions that have a real nonsingular soliton limit.

KdV equation elliptic finite gap solutions pole dynamics Calogero-Moser 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Bernard Deconinck
    • 1
  • Harvey Segur
    • 2
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleU.S.A.
  2. 2.Department of Applied MathematicsUniversity of ColoradoBoulderU.S.A.

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