Elastic (stretching) flows of null curves are studied in three-dimensional Minkowski space. As a main tool, a natural type of moving frame for null curves is introduced, without use of the pseudo-arclength. This new frame is related to a Frenet null frame by a gauge transformation that belongs to the little group contained in the Lorentz group SO(2, 1) and provides an analog of the Hasimoto transformation (relating a parallel frame to a Frenet frame for curves in Euclidean space). The Cartan structure equations of the transformed frame are shown to encode a hereditary recursion operator giving a two-component generalization of the recursion operator of Burgers equation, as well as a generalization of the Cole-Hopf transformation. Three different hierarchies of integrable systems are obtained from the various symmetries of this recursion operator. The first hierarchy contains two-component Burgers-type and nonlinear Airy-type systems; the second hierarchy contains novel quasilinear Schrödinger-type (NLS) systems; and the third hierarchy contains semilinear wave equations (in two-component system form). Each of these integrable systems is shown to correspond to a geometrical flow of a family of elastic null curves in three-dimensional Minkowski space.

在三维Minkowski空间中研究零曲线的弹性（拉伸）流动。作为主要工具，引入了用于零曲线的自然类型的移动框架，而无需使用伪弧长。此新框架通过规范转换与Frenet空框架相关，该规范归于Lorentz组SO（2 ，1），并提供了Hasimoto变换的模拟（将平行框架与Frenet框架相关联，用于欧氏空间中的曲线）。示出了经变换的帧的Cartan结构方程以对遗传递归算子进行编码，该遗传递归算子给出了Burgers方程的递归算子的两部分概括，以及对Cole-Hopf变换的概括。从此递归运算符的各种对称性获得了三个不同的可积系统层次。第一层包含两部分的Burgers型系统和非线性Airy型系统。第二层包含新颖的拟线性薛定ding型（NLS）系统；第三层包含半线性波动方程（以两组分系统形式）。