Journal of Nonlinear Science

, Volume 13, Issue 5, pp 487–517 | Cite as

Integrable Equations Arising from Motions of Plane Curves. II

  • K.-S. Chou
  • C.-Z. Qu
Regular Article

Integrable equations satisfied by the curvature of plane curves or curves on the real line under inextensible motions in some Klein geometries are identified. These include the Euclidean, similarity, and projective geometries on the real line, and restricted conformal, conformal, and projective geometries in the plane. Together with Chou and Qu [Physica D 162 (2002), 9–33], we determine inextensible motions and their associated integrable equations in all Klein geometries in the plane. The relations between several pairs of these geometries provide a natural geometric explanation of the existence of transformations of Miura and Cole-Hopf type.


Integrable Equation Real Line Projective Geometry Plane Curf Geometric Explanation 
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Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  • K.-S. Chou
    • 1
  • C.-Z. Qu
    • 2
  1. 1.Department of Mathematics, The Chinese University of Hong Kong, Hong KongP. R. China
  2. 2.Department of Mathematics, Northwest University, Xi’an, 71006P. R. China

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