On the dynamics of a continuum spin system

Lakshmanan, M.; Ruijgrok, Th.W.; Thompson, Colin J.

doi:10.1016/0378-4371(76)90106-0

Cited by 224 publications

(127 citation statements)

References 7 publications

Supporting

Mentioning

126

Contrasting

Order By: Relevance

“…It was proved in [5] that, among other conditions, the divergence of the integral In [8] we looked at self-similar solutions of (1) with respect to the unique scaling that preserves arclength. In this case, it can be easily proved -see [4], [16], and [17]-that…”

Section: Introductionmentioning

confidence: 93%

Self-similar solutions of the localized induction approximation: singularity formation

Gutiérrez

Vega

2004

Nonlinearity

View full text Add to dashboard Cite

Contents 1. Introduction 2. Proofs of the Theorems 2.1. Convergence to the initial data 2.2. Asymptotics 2.3. Scattering problem for the curve G 3. Properties of the curvature and torsion associated to the curve G 4. Self-similar solutions of the Cubic Non-linear Schrödinger equation 5. Further results 5.1. Symmetric solutions 5.2. On an ill-posedness result for the initial value problem associated to cubic Schrödinger equations 54 5.3. On the ill-posedness of the Localized Induction Approximation References

show abstract

Section: Introductionmentioning

confidence: 93%

Self-similar solutions of the localized induction approximation: singularity formation

Gutiérrez

Vega

2004

Nonlinearity

View full text Add to dashboard Cite

show abstract

“…To be more precise, κ ∝ Ja 2 , J being the coupling strength that measures the interaction between nearest neighbors in the isotropic Heisenberg model [21]. Once again a is the lattice constant.…”

Section: Modelmentioning

confidence: 99%

Correlation effects in the stochastic Landau-Lifshitz-Gilbert equation

Bose

Trimper

2010

Phys. Rev. B

View full text Add to dashboard Cite

We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time τ . The mean value for the spin wave components offers that the spin-wave dispersion relation and its damping is strongly influenced by the deterministic Gilbert damping parameter α, the strength of the stochastic forces D and its temporal range τ . The spin-spin-correlation function can be calculated in the low correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the α − D plane for different values of τ where damped spin wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin-waves. The onset is characterized by a critical value of the correlation time. An enhancement of τ leads to an increase of the oscillations of the correlation function.

show abstract

“…In [9], the system (1.4) with a = Q was derived as a continuum model of the classical Heisenberg spin system. The initial value problem for it was considered and the existence of a unique solution was obtained by Sulem et al [17].…”

Section: S For *¥ = K(st)exp(i$i(st)ds + Iq(t)mentioning

confidence: 99%

Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow

Tani¹,

Nishiyama²

1997

Publ. Res. Inst. Math. Sci.

View full text Add to dashboard Cite

It is known that the motion of a vortex filament with axial flow in a perfect fluid is approximately described by a generalization of the localized induction equation. The unique solvability of the initial value problem for it is first established by parabolic regularization. (1.2)x t = x s x x ss + a{x sss 4-(3/2)* ss x (x s x x ss )}, when the vortex filament has an axial flow within its thin vortex core. Here a is a real constant representing the magnitude of the axial flow effect.

show abstract

On the dynamics of a continuum spin system

Cited by 224 publications

References 7 publications

Self-similar solutions of the localized induction approximation: singularity formation

Self-similar solutions of the localized induction approximation: singularity formation

Correlation effects in the stochastic Landau-Lifshitz-Gilbert equation

Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow

Contact Info

Product

Resources

About