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The KP equation with quasiperiodic initial data. (English) Zbl 0938.35165
Summary: The Kadomtsev-Petviashvili (KP) equation is known to admit exact, quasiperiodic solutions that can be written in terms of Riemann theta functions, with a finite number of phases in each solution. In this paper, we propose a method to solve the initial-value problem for the KP equation, for initial data taken from this class of quasiperiodic functions.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35B15Almost and pseudo-almost periodic solutions of PDE
35C05Solutions of PDE in closed form
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
14H42Theta functions; Schottky problem
37K20Relations of infinite-dimensional systems with algebraic geometry, etc.