复$δ$势对非线性波的非对称完全吸收和激射
Asymmetric perfect absorption and lasing of nonlinear waves by a complex $δ$-potential
摘要：
谱奇异性和相干完全吸收是两个相互关联的概念，最初被引入和研究的线性波与复势相互作用。与此同时，完全吸收波的独特的渐近行为建议考虑这些现象的可能的推广为非线性波。在这里，我们解决完美的吸收非线性波由一个理想化的无限窄的耗散潜力的狄拉克$δ$ -功能与虚振幅。我们的主要结果是完全吸收流的存在，其空间振幅分布是不对称的吸收体的位置。这些非对称状态没有线性对应物。其线性稳定性进行了数值验证。非线性波导也支持对称和恒定振幅的完全吸收流。后一种类型的解决方案的稳定性可以确认分析。
英文摘要：
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic behavior of perfectly absorbed waves suggests considering possible generalizations of these phenomena for nonlinear waves. Here we address perfect absorption of nonlinear waves by an idealized infinitely narrow dissipative potential modeled by a Dirac $δ$-function with an imaginary amplitude. Our main result is the existence of perfectly absorbed flows whose spatial amplitude distributions are asymmetric with respect to the position of the absorber. These asymmetric states do not have a linear counterpart. Their linear stability is verified numerically. The nonlinear waveguide also supports symmetric and constant-amplitude perfectly absorbed flows. The stability of solutions of the latter type can be confirmed analytically.
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