  We derive a generalized Ginzburg-Landau (GL) functional near the tricritical
point in the (T,H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) superconducting state, in 1,2, and 3 dimensions. We find that the
transition from the normal to the FFLO state is of second order in 1 and 2
dimensions, and the order parameter with one-coordinate sine modulation
corresponds to the lowest energy near the transition line. We also describe in
the one-dimensional case the transformation of the sine modulation into the
soliton-lattice state as the magnetic field decreases. In 3 dimensions however,
we find that the transition into an FFLO state is of first order, and it is
impossible to obtain an analytic expression for the critical temperature. In
this case the generalized GL functional proposed here provides a suitable basis
for a numerical study of the properties of the FFLO state, and in particular
for computing the critical temperature, and for describing the transition into
a uniform state.
