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

J. Chen () and X. Geng

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 50, issue 3, 445-452

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 02.30.IK Integrable systems; 02.30.Jr Partial differential equations (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00156-3

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