Bragg spectroscopy of an accelerating condensate with solitary-wave behavior

We present a theoretical treatment of Bragg spectroscopy of an accelerating condensate in a solitary-wave state. Our treatment is based on the Gross-Pitaevskii equation with an optical potential representing the Bragg pulse and an additional external time-dependent potential generating the solitary-wave behavior. By transforming to a frame translating with the condensate, we derive an approximate set of equations that can be readily solved to generate approximate Bragg spectra. Our analytic method is accurate within a well-defined parameter regime and provides physical insight into the structure of the spectra. We illustrate our formalism using the example of Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap.