Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

摘要: Abstract We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula transformation. Secondly, use matrix analysis to avoid singularity of transformed potential functions find general nonsingular breather solutions. Moreover, limit process, deduce rogue wave solutions give classification by their dynamics including bright, dark, four-petals, two-peaks waves. Ever since coexistence dark soliton in non-zero background, naturally become quite appealing topic. Based on N -fold transformation, can explicit depict interactions. Finally, performing extensive simulations predict whether these solitons waves are stable enough propagate. These results be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, plasma physics.