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Integrable systems and invariant curve flows in centro-equiaffine symplectic geometry

Authors:	Junfeng Song Changzheng Qu

Institution:	^a Center for Nonlinear Studies, Northwest University, Xi’an, 710069, PR China ^b College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China ^c Department of Mathematics, Northwest University, Xi’an, 710069, PR China

Abstract:	In this paper, the theory for curves in centro-equiaffine symplectic geometry is established. Integrable systems satisfied by the curvatures of curves under inextensible motions in centro-equiaffine symplectic geometry are identified. It is shown that certain non-stretching invariant curve flows in centro-equiaffine symplectic geometry are closely related to the matrix KdV equations and their extension.

Keywords:	Invariant curve flow Integrable system Centro-equiaffine symplectic geometry Matrix KdV equations
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