Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics

Fiction Fix 04

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A new class of integrable surfaces associated with Bertrand curves

We present a new class of integrable surfaces associated with Bertrand curves. These surfaces are foliated by constant-torsion curves evolving according to a novel integrable geometric flow. Curves transverse to the constant-torsion curves (orbit curves) are Bertrand curves on the surface. The surfaces discussed interpolate two known integrable systems and we establish the connection. We also use tools from soliton theory to generate surface solutions using B\"{a}cklund transformations.Non UBCUnreviewedAuthor affiliation: Drexel UniversityFacult