  We investigate bright solitons in the one-dimensional Schr\"odinger equation
in the framework of an extended variational approach. We apply the latter to
the stationary ground state of the system as well as to coherent collisions
between two or more solitons. Using coupled Gaussian trial wave functions, we
demonstrate that the variational approach is a powerful method to calculate the
soliton dynamics. This method has the advantage that it is computationally
faster compared to numerically exact grid calculations. In addition, it goes
far beyond the capability of analytical ground state solutions, because the
variational approach provides the ability to treat excited solitons as well as
dynamical interactions between different wave packets. To demonstrate the power
of the variational approach, we calculate the stationary ground state of the
soliton and compare it with the analytical solution showing the convergence to
the exact solution. Furthermore, we extend our calculations to nonstationary
solitons by investigating the breathing oscillations of excited solitons and
the coherent collisions of several wave packets in both the low- and
high-energy regime. Comparisons of the variational approach with numerically
exact simulations on grids reveal excellent agreement in the high-energy regime
while deviations can be observed for low energies.
