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Mathematics, Vol. 11, Pages 4539: A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation
Mathematics doi: 10.3390/math11214539
Authors: Wei Liu Yafeng Liu Junxuan Wei Shujuan Yuan
In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. 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.
