Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 369, Issue 1939, Pages 1280-1300Publisher
ROYAL SOC
DOI: 10.1098/rsta.2010.0319
Keywords
LLG equation; spin systems; integrability; chaos and patterns
Categories
Funding
- Department of Science and Technology (DST), Government of India
- DST
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The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well-known integrable soliton equations, including nonlinear Schrodinger and sine-Gordon equations. It can admit very many dynamical structures including spin waves, elliptic function waves, solitons, dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the physical and spin dimensions and the nature of interactions. An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation that forms a basic dynamical equation in the field of spintronics. This article will briefly review these developments as a tribute to Robin Bullough who was a great admirer of the LLG equation.
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