  A robust and efficient time integrator for dynamical tensor approximation in
the tensor train or matrix product state format is presented. The method is
based on splitting the projector onto the tangent space of the tensor manifold.
The algorithm can be used for updating time-dependent tensors in the given
data-sparse tensor train / matrix product state format and for computing an
approximate solution to high-dimensional tensor differential equations within
this data-sparse format. The formulation, implementation and theoretical
properties of the proposed integrator are studied, and numerical experiments
with problems from quantum molecular dynamics and with iterative processes in
the tensor train format are included.
