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We explore the form of rogue wave solutions in a select set of case examplesof nonlinear Schr\"odinger equations with variable coefficients. We focus onsystems with constant dispersion, and present three different models thatdescribe atomic Bose-Einstein condensates in different experimentally relevantsettings. For these models, we identify exact rogue wave solutions. Ouranalytical findings are corroborated by direct numerical integration of theoriginal equations, performed by two different schemes. Very good agreementbetween numerical results and analytical predictions for the emergence of therogue waves is identified. Additionally, the nontrivial fate of smallnumerically induced perturbations to the exact rogue wave solutions is alsodiscussed.

Rogue Waves In Nonlinear Schr\"odinger Models with Variable Coefficients: Application to Bose-Einstein Condensates