Evolution of curvature invariants and lifting integrability

[1]  Evelyne Hubert,et al.  Differential Algebra for Derivations with Nontrivial Commutation Rules , 2005 .

[2]  J. Sanders,et al.  Integrable Systems in n-dimensional Riemannian Geometry , 2003, math/0301212.

[3]  Changzheng Qu,et al.  Integrable equations arising from motions of plane curves , 2002 .

[4]  E. Mansfield Moving frames and differential algebra , 2002 .

[5]  Jan A. Sanders,et al.  Integrable Systems in Three-Dimensional Riemannian Geometry , 2002, J. Nonlinear Sci..

[6]  Jing Ping Wang A List of 1+1 Dimensional Integrable Equations and Their Properties , 2002 .

[7]  T. Ivey Integrable geometric evolution equations for curves , 2002 .

[8]  P. J. Olver,et al.  Foundations of Computational Mathematics: Moving frames — in geometry, algebra, computer vision, and numerical analysis , 2001 .

[9]  Elizabeth L. Mansfield,et al.  Algorithms for Symmetric Differential Systems , 2001, Found. Comput. Math..

[10]  R. S. Ward,et al.  Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces , 1999 .

[11]  P. Olver,et al.  Moving Coframes: II. Regularization and Theoretical Foundations , 1999 .

[12]  G. M. Beffa THE THEORY OF DIFFERENTIAL INVARIANTS AND KDV HAMILTONIAN EVOLUTIONS , 1999 .

[13]  P. Olver,et al.  Moving Coframes: I. A Practical Algorithm , 1998 .

[14]  G. M. Beffa On the Poisson geometry of the Adler-Gel’fand-Dikii brackets , 1996 .

[15]  Joel Langer,et al.  The planar filament equation , 1994, solv-int/9403001.

[16]  P. Santini,et al.  An elementary geometric characterization of the integrable motions of a curve , 1994 .

[17]  Nakayama,et al.  Integrability and the motion of curves. , 1992, Physical review letters.

[18]  Joel Langer,et al.  Poisson geometry of the filament equation , 1991 .

[19]  V. Sokolov,et al.  The Symmetry Approach to Classification of Integrable Equations , 1991 .

[20]  A. Jamiołkowski Book reviewApplications of Lie groups to differential equations : Peter J. Olver (School of Mathematics, University of Minnesota, Minneapolis, U.S.A): Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, XXVI+497pp. , 1989 .

[21]  G. Lamb,et al.  Solitons on moving space curves , 1977 .

[22]  H. Hasimoto,et al.  A soliton on a vortex filament , 1972, Journal of Fluid Mechanics.

[23]  Ar. Tresse,et al.  Sur les invariants différentiels des groupes continus de transformations , 1894 .