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A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation

Author

Listed:
  • Wei Liu

    (Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China)

  • Yafeng Liu

    (Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China)

  • Junxuan Wei

    (Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China)

  • Shujuan Yuan

    (College of Science, North China University of Science and Technology, Tangshan 063210, China)

Abstract

In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem L φ = ( ∂ 2 − v ∂ − λ u ) φ = λ φ x . By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived.

Suggested Citation

  • Wei Liu & Yafeng Liu & Junxuan Wei & Shujuan Yuan, 2023. "A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation," Mathematics, MDPI, vol. 11(21), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4539-:d:1273832
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