Integrable motions of curves in S1×RS1×R

In this paper, motions of non-stretching curves in some Klein geometries, determined by the transformation groups acting on S1×RS1×R, are studied. It is shown that several 1+1-dimensional integrable equations including the KdV, mKdV, defocusing mKdV, Sawada–Kotera, Burgers equations and their hierarchies arise naturally from motions of non-stretching curves in such geometries.