Changzheng Qu, Junfeng Song, Ruoxia Yao, “Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries”, SIGMA, 2013, том 9,001, 19 стр.

Эта публикация цитируется в 25 статьях

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

Changzheng Qu^a, Junfeng Song^b, Ruoxia Yao^c

^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

Аннотация: 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.

Ключевые слова: invariant curve flow; integrable system; Euclidean geometry; Möbius sphere; dual Schrödinger equation; multi-component modified Camassa–Holm equation.

MSC: 37K10; 51M05; 51B10

Поступила: 28 сентября 2012 г.; в окончательном варианте 27 декабря 2012 г.; опубликована 2 января 2013 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2013.001