Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine–Gordon equation. The weakly damped oscillation of the sine–Gordon kink, named as the kink quasimode, is described explicitly. It is shown that the oscillatory kink behavior and the wave packet generation depend significantly on the initial nonequilibrium kink profile. In order to specify conditions of the generation of wobbling kinks with a multibreather structure we reformulate the direct scattering problem associated with the sine-Gordon equation as the spectral problem of the Schrödinger operator. We obtain the dependence of the radiation energy, which is emitted during formation of the multi-frequency wobbling kink, on the effective dimension of its initial profile.

中文翻译：

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通过振荡正弦-戈登系统中的扭结产生波包和通气孔

根据sine-Gordon方程的复杂扭结解，研究了非平衡不均匀性和拓扑缺陷的演化。明确描述了正弦-戈登扭结的弱阻尼振荡，称为扭结准模。结果表明，振荡扭结行为和波包的产生很大程度上取决于初始的非平衡扭结轮廓。为了指定具有多呼吸结构的摆动扭结的产生条件，我们将与正弦-戈登方程相关的直接散射问题重新公式化为薛定ding算子的频谱问题。我们获得了在多频摆动扭结形成期间所发射的辐射能量对其初始轮廓的有效尺寸的依赖性。