Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation

Details Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation

1999-03-26

arxiv.org/abs/solv-int/9904001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, 12 figures. Submitted for publication

Scientific paper

The real, nonsingular elliptic solutions of the Korteweg-deVries 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 shown to be 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.

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