The nonlinear effect of the energy localization on topological inhomogeneities is investigated in the sine-Gordon systems. The regimes of nonlinear oscillations of nonequilibrium configurations of domain walls in the quasi-one-dimensional ferromagnet are described in terms of kink and breather solutions of the sine-Gordon equation. The conditions of the energy localization, i.e., the formation of breather excitations on these topological inhomogeneities, are found for the initial configurations of the dilated double kink structures. The results are obtained in the framework of the Schrödinger-type equation of the direct scattering problem associated with the sine-Gordon equation. It is shown that the final state of the evolution of the nonequilibrium topological spin structure represents the multi-frequency precessing domain wall in the ferromagnet, which radiates the continuous spectrum waves.

中文翻译：

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正弦-戈登系统中拓扑结构的非线性振荡

在正弦-戈登系统中研究了能量局部化对拓扑不均匀性的非线性影响。准一维铁磁体中畴壁非平衡构型的非线性振荡机制用正弦-戈登方程的扭结和呼吸器解来描述。对于膨胀双扭结结构的初始配置，发现了能量定位的条件，即在这些拓扑不均匀性上形成呼吸激发。结果是在与正弦-戈登方程相关的直接散射问题的薛定谔型方程的框架内获得的。