Motion of general non-null curve in Minkowski 3-spaces associated with Landau-Lifshitz equation

Abstract

In that paper, firstly, we get two additional different non-null space curve evolutions in Minkowski 3-space by considering Landau-Lifshitz (LL) equation where we identify the spin vector with the binormal vector and the normal vector of these curves, respectively. Then, we obtain some links for constructing the moving non-null space curves by using the integrable LL equation. Finally, we give as an application the exact solution of the moving non-null curve evolutions obtained by taking the spin vector, the normal vector of the curve, and we showed graphically that these solutions are wave solutions.