High-order rogue wave and mixed interaction patterns for the three-component Gross-Pitaevskii equations in F=1 spinor Bose-Einstein condensates

Under investigation are the three-component Gross-Pitaevskii equations in F = 1 spinor Bose-Einstein condensates. Various localized waves' generation mechanisms have been derived from plane wave solutions using modulation instability. The perturbed continuous waves produce a large number of rogue wave structures through the split -step Fourier numerical method. Based on the known Lax pair, we construct the generalized iterative ( n , N - n )-fold Darboux transformation to generate various high -order solutions, including the bright-darkbright structure of rogue waves, periodic waves, and their mixed interaction structures. Numerical simulations show that rogue waves with a two-peaked structure have robust noise resistance and stable dynamical behavior. The asymptotic states of high -order rogue waves as the parameter approaches infinity are also predicted using the large parameter asymptotic technique. In addition, the position of these localized wave patterns can be controlled by some special parameters. These results may help us understand the dynamic behavior of spinor condensates for the mean-field approximation.