on infinite 2D and 3D systems [@mineev_helical_1994; @loder_superconductivity_2013; @dimitrova_theory_2007; @houzet_quasiclassical_2015; @zwicknagl_critical_2017; @agterberg_magnetic-field-induced_2007; @barzykin_inhomogeneous_2002; @kaur_helical_2005].

In this paper, we investigate the formation of inhomogeneous superconductivity in the presence of spin-orbit interaction and Zeeman (or exchange) field $\vec{h}$ for the particular situation of one-dimensional systems. We consider a superconducting wire deposited on a substrate (Fig. \[schema\_system\]). In this geometry, the modulation may occur only along the wire direction $x$, and the vector $\vec{n}$ is normal to the substrate (along $y$). This implies that the field $\vec{h}$ must have a component along the third direction, here $z$, in order to observe the effects related to the coupling Eq. (\[GL\]). Moreover, in the case of the exactly quadratic electron spectrum, 1D systems have a peculiar behavior: the modulated phase also requires a non zero component along the wire direction [@mironov_double_2015]. Consequently, the component $h_x$ of the field is also required to generate the nonuniform phase [@nesterov_anomalous_2016; @ojanen_magnetoelectric_2012]. Using the Green’s function formalism, we provide a self-consistent study of the effect of the magnetic field orientation on the field-temperature phase diagram of 1D systems both in the weak and strong spin-orbit coupling regimes. Our model is also relevant for quasi-1D superconductors like some organic superconductors 