  The possibility to observe and manipulate Majorana fermions as end states of
one-dimensional topological superconductors has been actively discussed
recently. In a quantum wire with strong spin-orbit coupling placed in proximity
to a bulk superconductor, a topological superconductor has been expected to be
realized when the band energy is split by the application of a magnetic field.
When a periodic lattice modulation is applied multiple topological
superconductor phases appear in the phase diagram. Some of them occur for
higher filling factors compared to the case without the modulation. We study
the effects of phase jumps and argue that the topologically nontrivial state of
the whole system is retained even if they are present. We also study the effect
of the spatial modulation in the hopping parameter.
