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我们提出了二维自相似变换理论, 以聚焦的(2 + 1)维NLS方程(数学称为抛物型的非线性微分方程)为模型, 构建了它被转变为聚焦的(1 + 1)维NLS方程的二维自相似变换, 深入研究了它的空间怪波激发, 发现除了(1 + 1)维NLS方程的Peregrine孤子、高阶怪波和多怪波诱导的线怪波所具有的短寿命特征外, 由Akhmediev呼吸子(AB)和Kuznetsov-Ma孤子(KMS)诱导的线怪波也具有这种短寿命特征. 这与由亮孤子(包括多孤子)诱导的空间相干结构保持形状和幅值不变的演化特征完全不同. 通过图示展现了本文例举的各类线怪波的演化规律. 本文揭示的线怪波激发新机制, 有助于提升对高维非线性波动模型的相干结构的新认识.A two-dimensional self-similarity transformation theory is established, and the focusing (parabolic) (2 + 1)-dimensional NLS equation is taken as the model. The two-dimensional self-similarity transformation is proposed for converting the focusing (2 + 1)-dimensional NLS equation into the focusing (1 + 1) dimensional NLS equations, and the excitation of its novel line-rogue waves is further investigated. It is found that the spatial coherent structures induced by the Akhmediev breathers (AB) and Kuznetsov-Ma solitons (KMS) also have the short-lived characteristics which are possessed by the line-rogue waves induced by the Peregrine solitons, and the other higher-order rogue waves and the multi-rogue waves of the (1 + 1) dimensional NLS equations. This is completely different from the evolution characteristics of spatially coherent structures induced by bright solitons (including multi-solitons and lump solutions), with their shapes and amplitudes kept unchanged. The diagram shows the evolution characteristics of all kinds of resulting line rogue waves. The new excitation mechanism of line rogue waves revealed contributes to the new understanding of the coherent structure of high-dimensional nonlinear wave models.
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Keywords:
- rogue wave/
- line rogue wave/
- two-dimensional self-similar transformation/
- nonlinear Schrödinger equation
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