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

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  • J. Chen
  • X. Geng

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

Suggested Citation

  • J. Chen & X. Geng, 2006. "Some quasi-periodic solutions to the Kadometsev-Petviashvili and modified Kadometsev-Petviashvili equations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(3), pages 445-452, April.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:3:p:445-452
    DOI: 10.1140/epjb/e2006-00156-3
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