Multi-Component Nonlinear Waves in Optics and Atomic Condensates: Theory, Computations and Experiments

Monday, October 31, 2016 - 3:15pm - 4:05pm
Keller 3-180
Panayotis Kevrekidis (University of Massachusetts)
Motivated by work in nonlinear optics, as well as more recently
in Bose-Einstein condensate mixtures, we will explore a
series of nonlinear states that arise in such systems. We
will start from a single structure, the so-called dark-bright solitary wave, and then
expand our considerations to multiple such waves, their
spectral properties, nonlinear interactions and experimental
observations. A twist will be to consider the dark
solitons of the one component as effective potentials that will trap the bright
waves of the second component, an approach that will also prove useful in characterizing
the bifurcations and instabilities of the system.
Beating so-called dark-dark soliton variants of such states
will also be touched upon. Generalizations of all these notions
in higher dimensions and, so-called, vortex-bright solitons
will also be offered and challenges for future work will be discussed.