Journal ArticleDOI
Equation of motion for the Heisenberg spin chain
G. R. W. Quispel,H.W. Capel +1 more
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TLDR
In this article, a systematic treatment of the equation of motion of the classical anisotropic Heisenberg spin chain is given, both in the discrete case and in the continuum limit, in which the spins associated with the lattice sites m are replaced by a spin density S(x, t), which is a function of the time t and the position x on the chain.Abstract:
A systematic treatment is given of the equation of motion of the classical anisotropic Heisenberg spin chain, both in the discrete case and in the continuum limit in which the spins Sm(t) associated with the lattice sites m are replaced by a spin density S(x, t), which is a function of the time t and the position x on the chain. In the case of axial symmetry the equation of motion for the spins is shown to be equivalent to a new equation in terms of one real variable, i.e. qm(t) in the discrete case q(x, t) in the continuum limit. (From the treatment by A.E. Borovik it follows that the new equation of motion for q(x, t) is completely integrible in the special case of quadratic anisotropy.) Explicit expressions are given for the Lagrangians, both in the ferromagnetic and in the antiferromagnetic case. The relation with the nonlinear Schrodinger equation on the one hand and the sine-Gordon equation on the other hand is discussed in some detail.read more
Citations
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Soliton solutions for quasilinear Schrödinger equations, II
TL;DR: For a class of quasilinear Schrodinger equations, the authors established the existence of ground states of soliton-type solutions by a variational method for soliton type solutions.
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On the existence of soliton solutions to quasilinear Schrödinger equations
TL;DR: In this article, the existence of standing wave solutions for quasilinear Schrodinger equations with strongly singular nonlinearities was proved using the calculus of variations and the Mountain Pass Theorem.
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Soliton solutions for quasilinear Schrödinger equations, I
Jiaquan Liu,Zhi-Qiang Wang +1 more
TL;DR: For a class of quasilinear Schrodinger equations, this paper established the existence of ground states of soliton type solutions by a minimization argument for soliton types.
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Soliton solutions for generalized quasilinear Schrödinger equations
Yaotian Shen,Youjun Wang +1 more
TL;DR: In this article, the existence of nontrivial solutions for generalized quasilinear Schrodinger equations which appear from plasma physics, as well as high-power ultrashort laser in matter is studied.
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Soliton solutions for quasilinear Schrödinger equations with critical growth
TL;DR: In this paper, the authors established the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth by using a change of variables, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem.
References
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Journal ArticleDOI
Field dependence of the intrinsic domain magnetization of a ferromagnet
T. Holstein,H. Primakoff +1 more
TL;DR: In this article, the intrinsic domain magnetization of a ferromagnetic with the external magnetic field was obtained, and an approximation to low temperatures and equivalent to those used by Bloch in his derivation of the ${T}^{1}$ law, were introduced.
Journal Article
Metastable States of Two-Dimensional Isotropic Ferromagnets
Journal ArticleDOI
Continuum spin system as an exactly solvable dynamical system
TL;DR: In this paper, it was shown that the one-dimensional classical spins with nearest neighbor Heisenberg interaction is an exactly solvable system and its dynamics describable by the nonlinear Schrodinger equation.
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