Two-Component Wadati--Konno--Ichikawa Equation and Its Symmetry Reductions

Chin. Phys. Lett.

2004, Vol. 21

Issue (11): 2077-2080 DOI:

Original Articles

Two-Component Wadati--Konno--Ichikawa Equation and Its Symmetry Reductions

QU Chang-Zheng¹;YAO Ruo-Xia^1,2;LI Zhi-Bin²

¹Centre for Nonlinear Studies, Northwest University, Xi’an 710069 ²Department of Computer Science, East China Normal University, Shanghai 200062

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QU Chang-Zheng, YAO Ruo-Xia, LI Zhi-Bin 2004 Chin. Phys. Lett. 21 2077-2080

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Abstract It is shown that two-component Wadati--Konno--Ichikawa (WKI) equation, i.e.~a generalization of the well-known WKI equation, is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg--de Vries flow. Group-invariant solutions of the two-component WKI equation which corresponds to an optimal system of its Lie point symmetry groups are obtained, and its similarity reductions to systems of ordinary differential equations are also given.

Keywords: 02.40.-k 03.40.Kf 02.30.Jr 04.20.Jb

Published: 01 November 2004

PACS:	02.40.-k	(Geometry, differential geometry, and topology)
	03.40.Kf
	02.30.Jr	(Partial differential equations)
	04.20.Jb	(Exact solutions)

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https://cpl.iphy.ac.cn/ OR https://cpl.iphy.ac.cn/Y2004/V21/I11/02077

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