The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation l...The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.展开更多
Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. ...Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.展开更多
文摘The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
基金The project supported by National Natural Science Foundation of China under Grant No.10574163
文摘Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.
