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Canonical Variables for Multiphase Solutions of the KP Equation
Author(s) -
Deconinck Bernard
Publication year - 2000
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00135
Subject(s) - integrable system , quasiperiodic function , mathematics , hamiltonian system , hamiltonian (control theory) , mathematical physics , initial value problem , mathematical analysis , riemann hypothesis , canonical form , pure mathematics , mathematical optimization
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.