Integrable flows on null curves in the anti-de Sitter 3-space (Q6623091)

The authors study integrable geometric flows defined on null curves without inflection points in the three-dimensional anti-de Sitter space. Such curves can canonically be parametrized by a ``proper time'' parameter and can be described through a differential invariant called bending. It is proved that the motion of a null curve induced by the so-called LIEN flow leads to the KdV equation for the bending of the curve. This result is naturally extended to a class of geometric flows with coefficients being certain differential polynomials of the bending that gives rise to the whole KdV hierarchy. The established interrelation between the LIEN flow and the KdV allows the authors to obtain analytically or numerically the null curves that correspond to either elliptic traveling wave solutions or a three-parameter family of periodic solutions to the latter equation.\N\NThe paper will be of interest to the narrow audience of experts in integrable systems or to differential geometers.