  We show that an unconventional superfluid triggered by spin-orbit coupling is
realized for repulsively interacting quasi-one-dimensional fermions. A
competition between spin-singlet and -triplet pairings occurs due to the
breaking of inversion symmetry. We show that both superfluid correlations decay
algebraically with the same exponent except for special coupling constants for
which a dominant superfluid is controlled by the spin-orbit coupling. We also
discuss a possible experiment to observe such phases with cold atoms.
