  We investigate dynamics arising after an interaction quench in the quantum
sine-Gordon model for a one-dimensional system initially prepared in a
spatially inhomogeneous domain wall state. We study the time-evolution of the
density, current and equal time correlation functions using the truncated
Wigner approximation (TWA) to which quantum corrections are added in order to
set the limits on its validity. For weak to moderate strengths of the
back-scattering interaction, the domain wall spreads out ballistically with the
system within the light cone reaching a nonequilibrium steady-state
characterized by a net current flow. A steady state current exists for a quench
at the exactly solvable Luther-Emery point. The magnitude of the current
decreases with increasing strength of the back-scattering interaction. The
two-point correlation function of the variable canonically conjugate to the
density reaches a spatially oscillating steady state at a wavelength inversely
related to the current.
