Skip to main content
Log in

Integrable Equations Arising from Motions of Plane Curves. II

Journal of Nonlinear Science Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Communicated by T. Fokas

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chou, KS., Qu, CZ. Integrable Equations Arising from Motions of Plane Curves. II. J. Nonlinear Sci. 13, 487–517 (2003). https://doi.org/10.1007/s00332-003-0570-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00332-003-0570-0

Keywords

Navigation