  A hybrid discrete-continuous model of layered superconductors with interlayer
Josephson couplings of arbitrary range is constructed. The conditions required
by gauge invariance and thermodynamical stability of the model are determined.
Some important special cases, in particular transition to the classic
Lawrence-Doniach model, are discussed. The conditions for presence of
alternating solutions and the posibilities to describe such states of a
superconductor by the continuum or bi-continuum models are examined. The
enhancement of superconductivity caused by the presence of higher order
Josephson couplings is shown.
