  We study theoretically the onset of nonuniform superconductivity in a
one-dimensional single wire in presence of Zeeman (or exchange field) and
spin-orbit coupling. Using the Green's function formalism, we show that the
spin-orbit coupling stabilizes modulated superconductivity in a broad range of
temperatures and Zeeman fields. We investigate the anisotropy of the
temperature-Zeeman field phase diagram, which is related to the orientation of
the Zeeman field. In particular, the inhomogeneous superconducting state
disappears if this latter field is aligned or perpendicular to the wire
direction. We identify two regimes corresponding to weak and strong spin-orbit
coupling respectively. The wave-vector of the modulated phase is evaluated in
both regimes. The results also pertain for quasi-1D superconductors made of
weakly coupled 1D chains.
