Canonical variables for multiphase solutions of the KP equation

Abstract

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.