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Zbl 0938.35165
Deconinck, Bernard; Segur, Harvey
The KP equation with quasiperiodic initial data. (English)
[J] Physica D 123, No.1-4, 123-152 (1998). ISSN 0167-2789

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 2000:: *35Q53 KdV-like equations
35B15 Almost periodic solutions of PDE
35C05 Solutions of PDE in closed form
37K10 Completely integrable systems etc.
14H42 Theta functions
37K20 Relations with algebraic geometry, etc.

Keywords: Kadomtsev-Petviashvili equation; Riemann surface; exact, quasiperiodic solutions; initial-value problem

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