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 $\delta$-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.

中文翻译：

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非线性波的非对称完美吸收和激光复数 δ 电位

光谱奇点和相干完美吸收是两个相互关联的概念，最初是为与复势相互作用的线性波而引入和研究的。同时，完全吸收波的独特渐近行为表明考虑这些现象对非线性波的可能推广。在这里，我们通过理想化的无限窄耗散势来解决非线性波的完美吸收问题，该势能由具有虚振幅的狄拉克 $\delta$ 函数建模。我们的主要结果是存在完全吸收的流动，其空间振幅分布相对于吸收体的位置不对称。这些不对称状态没有线性对应物。它们的线性稳定性通过数值验证。非线性波导还支持对称和等幅完美吸收流。后一种溶液的稳定性可以通过分析来确认。