In this work, we study a critical thermodynamic system, say, a simple fluid or a binary liquid mixture, of plane film geometry whose stable states, at given temperature and external ordering field, are determined by the minimizers of the one- dimensional counterpart of the standard φ4 Ginzburg-Landau Hamiltonian in terms of the order parameter. We focus on the case of Dirichlet-Dirichlet boundary conditions on the confining the fluid walls. Assuming that the boundaries of the system are positioned at a finite distance from one another, we solve the corresponding boundary-value problem of one nonlinear differential equation in terms of Weierstrass and Jacobi elliptic functions and give analytic representation of the order parameter profiles and of the local and total susceptibilities depending on the temperature and ordering field.
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