Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons

In the last decade, the concept of a dissipative soliton (DS), which is a strongly localized and stable coherent structure emergent in a nonlinear dissipative system far from the thermodynamic equilibrium, actively developed and became well established. This concept is highly useful in very different fields of science, ranging from field theory and cosmology, optics and condensed-matter physics, to biology and medicine [2, 13, 15, 16, 38, 52, 135, 255]. One may paraphrase: It is “apparent that solitons are around us. In the true sense of the word they are absolutely everywhere” [14]. Nonequilibrium character of a system where a DS emerges, requires a well-organized energy exchange of DS with an environment. In turn, this energy flow forms a nontrivial internal structure of a soliton, which provides the energy redistribution inside it (e.g., see [13, 15, 257]). In this respect, a DS is a primitive analog of a cell.