  For the first time, we obtain the complete and exact analytical solution of
the Lawrence-Doniach model for layered superconductors in external parallel
magnetic fields. By solving a nontrivial mathematical problem of exact
minimization of the free-energy functional, we derive a closed, self-consistent
system of mean-field equations involving only two variables. Exact solutions to
these equations prove simultaneous penetration of Josephson vortices into all
the barriers, yield a completely new expression for the lower critical field,
refute the concept of a triangular Josephson vortex lattice and clarify the
physics of Fraunhofer oscillations of the total critical Josephson current.
  PACS numbers: 74.80.Dm, 74.20.De, 74.50.+r
