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

Vasil’ev, S. Kh.

C. R. Acad. Bulg. Sci. 42, No. 7, 19-22 (1989).

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

MSC:

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

Keywords:

algebraic curves; Kadomtsev-Petviashvili equation; Riemann theta function

Citations:

Zbl 0597.76018