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BIRS Workshop Lecture Videos

Modulated amplitude waves with nontrivial phase in quasi-1D inhomogeneous Bose-Einstein condensates Torres, Pedro J.


A modulated amplitude wave (MAW) is a coherent structure with double periodicity, both in the spatial and temporal variables. The aim of the talk is to present some recent results on the existence of MAWs with nontrivial phase in a quasi-1D inhomogeneous Bose-Einstein condensate (BEC) with external trapping. Physically, a non-trivial phase means some transport of matter, while mathematically it implies the presence of a singular term in the amplitude equation. For a single component BEC, we state and prove a general result without assuming any kind of sign condition on the trapping potential or the scattering length. For a multi-component BEC, we present some novel results where one of the component is stationary while the other ones are rotating. Basic tools on averaging theory and local continuation of non-degenerate solutions are used in the proofs.

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