  The objective of this work is the introduction and investigation of
favourable time integration methods for the Gross--Pitaevskii equation with
rotation term. Employing a reformulation in rotating Lagrangian coordinates,
the equation takes the form of a nonlinear Schr{\"o}dinger equation involving a
space-time-dependent potential. A natural approach that combines
commutator-free quasi-Magnus exponential integrators with operator splitting
methods and Fourier spectral space discretisations is proposed. Furthermore,
the special structure of the Hamilton operator permits the design of
specifically tailored schemes. Numerical experiments confirm the good
performance of the resulting exponential integrators.
