Some recent papers (abstracts, PDF and PostScript files):

• Recursion in curve geometry, New York Journal of Mathematics, 5 (1999) 25-51.
  Abstract: Recursion schemes are familiar in the theory of soliton equations, e.g., in the discussion of infinite hierarchies of conservation laws for such equations. Here we develop a variety of special topics related to curves and curve evolution in two and three-dimensional Euclidean space, with recursion as a unifying theme. The interplay between curve geometry and soliton theory is highlighted. Complete paper: PostScript, PDF
• Straightening soliton curves, Applied Math. Letters, to appear.
  Abstract: A canonical straightening process is described for soliton curves associated with the localized induction hierarchy. Following computer animated examples (see animated GIF Ribbon animation), the present topic is placed in the context of a larger theme: the soliton class is a natural setting for representation of diverse topological and geometrical behavior of curves and their motions. Complete paper: PostScript, PDF
• Taimanov's surface motion and a Backlund transformation for curves, Conformal Geometry and Dynamics, 3 (1999) 37-49 (with O. Garay).
  Abstract: Taimanov's evolution of conformally parametrized surfaces in Euclidean space by the modified Novikov-Veselov equation is interpreted here (in the revolution case) using hyperbolic geometry and Backlund transformations for curves. Complete paper: PostScript, PDF
• Geometric realizations of Fordy Kulish nonlinear Schrodinger systems, Pacific J. Math., to appear (with R. Perline).
  Abstract: A method of Sym and Pohlmeyer, which produces geometric realizations of many integrable systems, is applied to the Fordy-Kulish generalized non-linear Schrodinger systems associated with Hermitian symmetric spaces. The resulting geometric equations correspond to distinguished arclength-parametrized curves evolving in a Lie algebra, generalizing the localized induction model of vortex filament motion. An appropriate specialization yields evolution equations for curves in spheres and Euclidean space of any dimension, with natural curvatures satisfying a generalized mKdV system. Complete paper: PostScript, PDF