Eur. Phys. J. B 50, 445-452 (2006)
https://doi.org/10.1140/epjb/e2006-00156-3

Some quasi-periodic solutions to the Kadometsev-Petviashvili and modified Kadometsev-Petviashvili equations

Department of Mathematics, Zhengzhou University Zhengzhou 450052, Henan, P.R. China

Corresponding author: ^a jbchen@gs.zzu.edu.cn

Received: 22 September 2005
Revised: 6 December 2005
Published online: 5 May 2006

Abstract

The Kadometsev-Petviashvili (KP) and modified KP (mKP) equations are retrieved from the first two soliton equations of coupled Korteweg-de Vries (cKdV) hierarchy. Based on the nonlinearization of Lax pairs, the KP and mKP equations are ultimately reduced to integrable finite-dimensional Hamiltonian systems in view of the r-matrix theory. Finally, the resulting Hamiltonian flows are linearized in Abel-Jacobi coordinates, such that some specially explicit quasi-periodic solutions to the KP and mKP equations are synchronously given in terms of theta functions through the Jacobi inversion.