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 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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2023-11, Vol.11 (21), p.4539
Main Authors: Liu, Wei, Liu, Yafeng, Wei, Junxuan, Yuan, Shujuan
Format: Article
Language:English
Subjects:
Coordinates
Differential equations
Eigenvalues
Euler-Lagrange equation
involutive solution
Kadometsev–Petviashvili equation
Mathematical analysis
Mathematical functions
Nonlinear equations
nonlinearization of Lax pairs
Partial differential equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11214539