Strong/weak duality symmetries for Jacobi--Gordon field theory through elliptic functions

By using the scheme of Jacobi elliptic functions with their duality symmetries we present a formulation of the Jacobi- Gordon field theory that will manifest the strong/weak coupling duality at classical level; for certain continuous limits for the elliptic modulus the model will reduce to the standard sin/sinh Gordon field theories, for which such a strong/weak duality is known only at the level of the S-matrix. It is shown that the so called self-dual point for the standard sin/sinh Gordon field theory that divides the strong and the weak coupling regimes, corresponds only to one point of a set of fixed points under the duality transformations for the elliptic functions. The potentials constructed in terms of elliptic functions have a critical behavior near that self-dual point, showing a change of topology; in the weak coupling regime the vacuum topology implies that there exists the possibility of formation of topological defects, and in the strong regime coupling there no exists the possibility of formation of those defects. Furthermore, the equations of motion can be solved in exact form in terms of the inverse elliptic functions; in a case the kink-like solitons asso\-cia\-ted with the maxima of the potential can decay to cusp-like solitons associated with the minima. The polynomial expansions of the generalized models show a critical behavior at certain self-dual points; such points define the regions where the spontaneous symmetry breaking scenarios are po\-ssi\-ble. By invoking the duality symmetries for the elliptic functions, an explicit relation between the original potentials and their dual versions are constructed; with this relationship, an approaching to a specific self-dual point is considered for our generalized models.