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Three-component WKI equation and curve motion flow in Euclidean and Minkowski space

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  • Zhang, Dongbo
  • Hou, Yuqing

Abstract

Motion of curves in the four-dimensional Euclidean and Minkowski space are discussed. It is shown that the three-component WKI equation and its hyperbolic type arise from certain curve motion flows. They are obtained by using the relation between curvatures of the curves and their graph. Group-invariant solutions to the three-component WKI equation and its hyperbolic type are also derived.

Suggested Citation

  • Zhang, Dongbo & Hou, Yuqing, 2007. "Three-component WKI equation and curve motion flow in Euclidean and Minkowski space," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 17-29.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:17-29
    DOI: 10.1016/j.chaos.2005.09.028
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