Abstract
By the similarity reduction and Darboux transformation, we derive higher-order modes of three-dimensional Bose–Einstein condensate modulation instability in the nonautonomous Gross–Pitaevskii equation and manipulate them by regulating the time-dependent potential and gain. Firstly, by the similarity reduction, the (3+1)-dimensional nonautonomous Gross–Pitaevskii equation reduces to a (1+1)-dimensional standard nonlinear Schrodinger equation with constant coefficients. Then, considering the Akhmediev breather solution as the first-order modulation instability solution of the higher-order modes of Bose–Einstein condensate modulation instability, we achieve the Nth-order (N = 2, 3, 4, and 5) modulation instability solutions by the Darboux transformation. Finally, we verify the stable higher-order modes of Bose–Einstein condensate modulation instability and manipulate them by direct numerical simulation. The obtained results may raise the possibility of related experiments and potential applications in Bose–E...
Published Version
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