Some Blow-Up and Smooth Solutions about Landau-Lifshitz Equation and Their Spatial Curvature Behavior

الملخص EN

We construct the exact solution of (2+1)-dimensional space-time Landau-Lifshitz equation (LLE) without the Gilbert term.

Under suitable transformations, some exact solutions are obtained in the radially symmetric coordinates and nonsymmetric coordinates.

The type of solutions cover the finite-time blow-up solution, smooth solution in time and vortex solution.

At the end, some properties about these solutions and their spatial curvature are illustrated by the graphs.