  We formulate an isoperimetric deformation of curves on the Minkowski plane,
which is governed by the defocusing mKdV equation. Two classes of exact
solutions to the defocusing mKdV equation are also presented in terms of the
$\tau$ functions. By using one of these classes, we construct an explicit
formula for the corresponding motion of curves on the Minkowski plane even
though those solutions have singular points. Another class give regular
solutions to the defocusing mKdV equation. Some pictures illustrating typical
dynamics of the curves are presented.

Differential Geometry;Exactly Solvable and Integrable Systems