  We develop a method for finding the time evolution of exactly solvable models
by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the
stationary Bethe wavefunction except for time varying Bethe parameters and a
complex phase prefactor. From this, we derive a set of first order nonlinear
coupled differential equations for the Bethe parameters, called the dynamical
Bethe equations. We find that this gives the exact solution to particular types
of exactly solvable models, including the Bose-Hubbard dimer and Tavis-Cummings
model. These models go beyond the Gaudin class, and offers an interesting
possibility for performing time evolution in exactly solvable models.
