We deal with solitons of the mean curvature flow. The definition of translating solitons on a light-like direction in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, translation surfaces, obtaining space-like and time-like, entire and not entire, complete and incomplete examples. Among them, all our time-like examples are incomplete. The second family consists of those which are invariant by a 1-dimensional subgroup of parabolic motions, i.e., with light-like axis. The classification result implies that all examples of this second family have singularities.

中文翻译：

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Minkowski 3 空间中平行光状方向上平移孤子的动物园

我们处理平均曲率流的孤子。介绍了在闵可夫斯基三空间中在类光方向上平移孤子的定义。首先，我们对图形、平移面、类时空、完整与不完整、完整与不完整示例进行分类。其中，我们所有的类时间例子都是不完整的。第二类由抛物线运动的一维子群不变的那些组成，即具有类似光的轴。分类结果意味着该第二族的所有示例都具有奇异性。