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

Wei Liu, Yafeng Liu (), Junxuan Wei and Shujuan Yuan
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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

Mathematics, 2023, vol. 11, issue 21, 1-10

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.

Keywords: nonlinearization of Lax pairs; Kadometsev–Petviashvili equation; involutive solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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