Quasi-periodic solutions for some \((2+1)\)-dimensional integrable models generated by the Jaulent-Miodek hierarchy
type: Item
instance of: scholarly article
zbMATH Open document ID: 0978.37054
DOI: 10.1088/0305-4470/34/5/305
author: Huihui Dai
author: Xianguo Geng
author: Cewen Cao
published in: Journal of Physics A: Mathematical and General
publication date: 2001-06-06T00:00:00Z
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K20
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 1602281
zbMATH Keywords: quasi-periodic solutions
zbMATH Keywords: integrable Hamiltonian systems
zbMATH Keywords: Riemann theta functions
zbMATH Keywords: Jaulent-Miodek hierarchy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/0305-4470/34/5/305
OpenAlex ID: W1982989780
title: Quasi-periodic solutions for some \((2+1)\)-dimensional integrable models generated by the Jaulent-Miodek hierarchy
review text: A couple of \(2+1\) dimensional integrable equations such as the modified Kadomtsev-Petviashvili equation are investigated, which are generated from the Jaulent-Miodek hierarchy. They are decomposed into compatible finite-dimensional integrable Hamiltonian systems, through an application of symmetry constraints to the Jaulent-Miodek spectral problem. Using the elliptic coordinates, the involutivity and the functional independence of integrals of motion are verified. Finally starting from the Able-Jacobi coordinates, quasi-periodic solutions to the resulting \(2+1\) integrable equations are derived by using the Riemann theta functions. The paper is clearly written and it is a supplement to a series of the authors' works on the topic.
reviewed by: Wen-Xiu Ma
description: scientific article; zbMATH DE number 1602281