  We study the isospin singlet pairing in asymmetric nuclear matter with
nonzero total momentum of the condensate Cooper pairs. The quasiparticle
excitation spectrum is fourfold split compared to the usual BCS spectrum of the
symmetric, homogeneous matter. A twofold splitting of the spectrum into
separate branches is due to the finite momentum of the condensate, the isospin
asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin
singlet and triplet paired states leads to further twofold splitting of each of
these branches. We solve the gap equation numerically in the isospin singlet
channel in the case where the pairing in the isospin triplet channel is
neglected and find nontrivial solutions with finite total momentum of the
pairs. The corresponding phase assumes a periodic spatial structure which
carries a isospin density wave at constant total number of particles. The phase
transition from the BCS to the inhomogeneous superconducting phase is found to
be first order and occurs when the density asymmetry is increased above 0.25.
The transition from the inhomogeneous superconducting to the unpaired normal
state is second order. The maximal values of the critical total momentum (in
units of the Fermi momentum) and the critical density asymmetry at which
condensate disappears are $P_c/p_F = 0.3$ and $\alpha_c = 0.41$. The possible
spatial forms of the ground state of the inhomogeneous superconducting phase
are briefly discussed.
