1998/11/09 by Bernard Deconinck, Deconinck, Bernard
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9811006
52 papes, 3 figures, uses psfig, latexsym
arxiv created 1998/11/09 · openalex publication_date 1998/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.