Fundamental domains of real-valued solutions of the KP equations. (English) Zbl 0682.35098

The fundamental domains of real valued solutions of the Kadomtsev- Petviashvili equation, based on a Riemann theta function of genus g are discussed. There are two types of KP equation, KP1 and KP2 which differs by the sign. The genus 2 and genus 3 solutions of KP1 and KP2 are given. These problems are also discussed by B. A. Dubrovin [The geometry of Abelian varieties, Riemann surfaces and nonlinear equations, Doctorate thesis, Moscow (1984)] and by H. Segur and A. Finkel [Stud. Appl. Math. 73, 183-220 (1985; Zbl 0597.76018)].
Reviewer: N.Kostov


35Q99 Partial differential equations of mathematical physics and other areas of application
30F20 Classification theory of Riemann surfaces
14K25 Theta functions and abelian varieties


Zbl 0597.76018