Finding topological solitary waves in models with non-equivalent vacua

We study the existence of bidimensional bosonic models for which the spontaneous symmetry breaking phenomenon yields, at classical level, non-equivalent vacua. Once we introduce the concept of vacuum manifold , defined in terms of the vacuum field configurations, the behavior of the models at issue can be analyzed by means of the so-called classical moduli space . The aforementioned structure allows us to classify the kink-like excitations into loops and links. To be precise, the loops interpolate smoothly between equivalent minima of the classical potential while the links connect vacua located at different points in . Although exact results are very hard to come by, we resort to models simple enough to provide us with the solitary waves in closed form.