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

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

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 b...

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Veröffentlicht in:ISRN applied mathematics 2012-01, Vol.2012 (2012), p.1-20
Hauptverfasser: Zhong, Penghong, Wang, Shu, Zeng, Ming
Format: Artikel
Sprache:eng
Schlagworte:
Construction
Curvature
Energy
Exact solutions
Fluid dynamics
Fluid flow
Graphs
Magnetic fields
Mathematical analysis
Methods
Ordinary differential equations
Studies
Transformations
Vortices
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Zusammenfassung: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.
ISSN:2090-5564
2090-5572
2090-5572
DOI:10.5402/2012/752964