  In the initial stage of relativistic heavy-ion collisions, strong magnetic
fields appear due to the large velocity of the colliding charges. The evolution
of these fields appears as a novel and intriguing feature in the
fluid-dynamical description of heavy-ion collisions. In this work, we study
analytically the one-dimensional, longitudinally boost-invariant motion of an
ideal fluid in the presence of a transverse magnetic field. Interestingly, we
find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite
conductivity, and irrespective of the strength of the initial magnetization,
the decay of the fluid energy density $e$ with proper time $\tau$ is the same
as for the time-honored "Bjorken flow" without magnetic field. Furthermore,
when the magnetic field is assumed to decay $\sim \tau^{-a}$, where $a$ is an
arbitrary number, two classes of analytic solutions can be found depending on
whether $a$ is larger or smaller than one. In summary, the analytic solutions
presented here highlight that the Bjorken flow is far more general than
formerly thought. These solutions can serve both to gain insight on the
dynamics of heavy-ion collisions in the presence of strong magnetic fields and
as testbeds for numerical codes.
