  We solve the problem of exact minimization of the Lawrence-Doniach (LD)
free-energy functional in parallel magnetic fields. We consider both the
infinite in the layering direction case (the infinite LD model) and the finite
one (the finite LD model). We prove that, contrary to a prevailing view, the
infinite LD model does not admit solutions in the form of isolated Josephson
vortices. For the infinite LD model, 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, accompanied by oscillations and jumps of the magnetization, and yield
a completely new expression for the lower critical field. Moreover, the
obtained equations allow us to make self-consistent refinements on such
well-known results as the Meissner state, Fraunhofer oscillations of the
critical Josephson current, the upper critical field, and the vortex solution
of Theodorakis [S. Theodorakis, Phys. Rev. B, v. 42, 10172 (1990)]. Our
consideration of the finite LD model illuminates the role of the boundary
effect. In contrast to the infinite case, an explicit analytical solution to
the Maxwell equations of the finite case does not preclude the existence of
localized Josephson vortex configurations. By the use of this solution, we
obtain a self-consistent description of the Meissner state. Finally, we discuss
some theoretical and experimental implications.
