Canonical variables for multiphase solutions of the KP equation

Details Canonical variables for multiphase solutions of the KP equation Canonical variables for multiphase solutions of the KP equation

1998-11-09

arxiv.org/abs/solv-int/9811006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

52 papes, 3 figures, uses psfig, latexsym

Scientific paper

The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of parameters is given for the description of each such solution. The Hamiltonian systems are completely integrable in the sense of Liouville. In effect, this provides a solution of the initial-value problem for the theta-function solutions. Some consequences of this approach are discussed.

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