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

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. [ABSTRACT FROM AUTHOR]