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 firstname.lastname@example.org
Revised: 6 December 2005
Published online: 5 May 2006
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.
PACS: 02.30.IK – Integrable systems / 02.30.Jr – Partial differential equations
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006