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Rogue waves are usually considered as the large amplitude waves that come from nowhere and disappear without trace. The formation of rogue waves are generally related to the degradation of breather solutions. In some special cases, a special form of the interactions between two solitons can be explained by the breather solutions. The types of soliton collisions are very rich, such as weak interactions, strong interactions, and solitons decay: rogue waves (the large amplitude waves that come from nowhere and disappear without trace), and partial-rogue waves (the large amplitude waves that come from nowhere but leave with a trace). Different from the rogue waves and partial-rogue waves, we mainly study the rogue wave type solutions (the large amplitude waves that come and leave with a trace) from the degeneracy in soliton solutions caused by the interactions of solitons synchronization and resonance in the Rotating reduced Maxwell–Bloch equations, which originated from circularly polarized light propagation on two isotropic electronic field components from optical system. These results systematically illustrate the formation of rogue wave type solutions in terms of boundary conditions, spectral parameters and the number of soliton interactions. [ABSTRACT FROM AUTHOR]

Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting appropriate functions of the general variable separation solution. [ABSTRACT FROM AUTHOR]

A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer-Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instanton-like and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution. [ABSTRACT FROM AUTHOR]