The field of nonlinear optics has been investigated extensively since its beginning in 1961. This development is in both the theory of nonlinear effects and the theory of nonlinear interactions in nonlinear media, and in the applications of nonlinear devices. The mathematical basis of nonlinear optics is Maxwell’s system of equations governing propagation of electromagnetic waves in a material medium, combined with relations accounting for the nonlinear response of the medium to the electromagnetic field. This review paper presents the contribution of African researchers to recent theoretical advances in the study of nonlinear interactions between electromagnetic waves with different types of nonlinear media, such as optical fibers, metamaterials, and Bose–Einstein condensates, that constitute a fascinating source of temporal, spatial, and spatiotemporal phenomena in the physics of light, and that lead to modulational instability, optical pulse compression, rogue waves, ${\cal P\!T}$-symmetric phenomena, supercontinuum generation, and dissipative solitons.

中文翻译：

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从非洲的“ tam-tam”到非线性光学[已邀请]

自1961年成立以来，非线性光学领域已经得到了广泛的研究。这种发展不仅在非线性效应理论和非线性介质中的非线性相互作用理论上，而且在非线性设备的应用中都得到了发展。非线性光学的数学基础是麦克斯韦方程组，该方程组控制电磁波在材料介质中的传播，并结合考虑介质对电磁场的非线性响应的关系。这篇评论文章介绍了非洲研究人员对电磁波与不同类型的非线性介质（例如光纤，超材料和玻色-爱因斯坦凝聚物）之间的非线性相互作用进行研究的最新理论进展，这些非线性介质构成了令人着迷的时间性来源，空间的$ {\ cal P \！T} $-对称现象，超连续谱的产生和耗散孤子。