Evolution of a solitary wave: optical soliton, soliton molecule and soliton crystal

Abstract This review embarks on a captivating odyssey of tracing the birth of light from the Big Bang to its intricate interplay with materials. It delves into the fundamental truth that nonlinearity is ubiquitous, and induces fascinating spatiotemporal structures, chaos, and complexity in the medium. After a brief exploration of waves and the effect of nonlinearity in diverse domains, the review article focuses on the field of photonics. This comprehensive review dives into the captivating physics of solitons. This study explores the formation of solitons in optical fibers due to specific nonlinear effects within the material, such as the Kerr effect, the fundamental behaviour of solitons in integrable models, diverse interactions, and the formation of intricate soliton molecules, soliton complexes, and soliton crystals within the dissipative optical systems. We analyse key research on optical solitons and highlight the control of optical solitons for advancements in communication systems, signal processing, optical computing, quantum technologies, etc. Through a meticulous research survey, we find that there is a limited understanding of weak soliton interactions. Further, more theoretical models to be investigated for exploring anisotropy of material and optomechanical interplay. Bridging these gaps will definitely propel future soliton research.