Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 752964, 20 pages
http://dx.doi.org/10.5402/2012/752964
Research Article

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

Department of Applied Mathematics, Beijing University of Technology, Ping Le Yuan 100, Chaoyang District, Beijing 100124, China

Received 30 May 2012; Accepted 26 June 2012

Academic Editors: S. Blanes and X.-S. Yang

Copyright © 2012 Penghong Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.