Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation

Susana Gutierrez, Andre De Laire

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
158 Downloads (Pure)


We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter.

We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schrödinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1D-Schrödinger map equation.
Original languageEnglish
Pages (from-to)1307-1350
Issue number5
Publication statusPublished - 17 Apr 2015


  • Landau–Lifshitz–Gilbert equation
  • ferromagnetic spin chain
  • Schrodinger maps
  • heat-flow for harmonic maps
  • self-similar solutions
  • asymptotics


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