Self-similar solutions to the curvature flow and its inverse on the 2-dimensional light cone

We consider a novel curvature flow for curves on the 2-dimensional light cone, contained in 3-dimensional Minkowski space. show that solutions to (CF) such are correspondence with inverse (ICF). prove ellipses and hyperbolas only evolve under homotheties. The closed ones they ancient solutions. spacelike curve cone is self-similar solution CF (resp. (ICF)) if, its of curvature) differs by constant c from being inner product between tangent vector field fixed v soliton when $$c=0$$ . each there exists 2-parameter family ICF, cone. Considering non-trivial CF, we corresponding ICF may have at most three connected components. Moreover, end either unbounded or it tends 0 c. Explicitly given included some visualized.