Abstract

Ricardo Carretero-Gonzalez and Keith Promislow
Dep. of Mathematics, Simon Fraser University, Burnaby, Canada

"Localized breathers in coupled Bose-Einstein condensates"

We present a treatment for the interaction of coupled Bose-Einstein condensates trapped in periodic potentials. Under certain physical conditions, the condensates dynamics may be described by the cubic nonlinear Schr\"odinger equation with a potential term. The corresponding multi-soliton solution is treated using variational/perturbation techniques to reduce the infinite-dimensional dynamics to a lattice differential equation on the soliton's parameters (position, width, height, phase, ...). By introducing a position-oscillating ansatz for the lattice dynamics it is possible to further reduce the system to a discrete map. This map corresponds to a recurrence relation between neighbouring amplitudes for the position-oscillation. A wide range of oscillatory behaviour is then obtained by following different orbits of the map. In particular, non-trivial fixed and periodic points give rise to extended homogeneous and modulated oscillations on the condensates positions. More interesting, however, is the occurrence of exponentially localized oscillations corresponding to homoclinic connections between the stable and unstable manifolds emanating from the trivial fixed point of the map.

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