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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 001, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.001 (Mi sigma784) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries

Changzheng Qua, Junfeng Songb, Ruoxia Yaoc

a Center for Nonlinear Studies, Ningbo University, Ningbo, 315211, P.R. China
b College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R. China
c School of Computer Science, Shaanxi Normal University, Xi’an, 710062, P.R. China
Full-text PDF (445 kB) Citations (24)
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DOI: https://doi.org/10.3842/SIGMA.2013.001
Abstract: In this paper, multi-component generalizations to the Camassa–Holm equation, the modified Camassa–Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa–Holm equation and the multi-component modified Camassa–Holm equation are provided. It is shown that these equations arise from non-streching invariant curve flows respectively in the three-dimensional Euclidean geometry, the two-dimensional Möbius sphere and $n$-dimensional sphere ${\mathbb S}^n(1)$. Integrability to these systems is also studied.
Keywords: invariant curve flow; integrable system; Euclidean geometry; Möbius sphere; dual Schrödinger equation; multi-component modified Camassa–Holm equation.
Received: September 28, 2012; in final form December 27, 2012; Published online January 2, 2013
Bibliographic databases:
Document Type: Article
MSC: 37K10; 51M05; 51B10
Language: English
Citation: Changzheng Qu, Junfeng Song, Ruoxia Yao, “Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries”, SIGMA, 9 (2013), 001, 19 pp.
Citation in format AMSBIB
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\by Changzheng~Qu, Junfeng~Song, Ruoxia~Yao
\paper Multi-Component Integrable Systems and~Invariant Curve Flows in Certain Geometries
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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