Abstract
The modulational instability of the coupled Gross–Pitaevskii equation (alias nonlinear Schrödinger equation), which describes two Bose–Einstein condensates trapped in an asymmetric double-well potential, is investigated. The nonlinear dispersion relation that relates the frequency and wave number of the modulating perturbations is found and its analysis shows several possibilities for the modulational stability region. Exact soliton and periodic solutions are constructed via elliptic ordinary differential equations.
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