Localised, stable structures known as solitons play a very important role in mathematical models of the physical world. In this work two different kinds of solitons are examined. The first are vortices in exciton-polariton Bose-Einstein condensates. Exciton-polariton condensates are a novel state of matter whose peculiar properties, among which very high spatio-temporal coherence, nearly frictionless flow, non-equilibrium, are dramatically influenced by the presence and behaviour of vortices. The second are gravitational instantons, Riemannian manifolds which are exact solutions of Euclidean Einstein equations in four dimensions. According to a recent and innovative proposal, known as the geometric models of matter framework, elementary particles are to be modelled by four-dimensional manifolds. Within this framework, asymptotically locally flat gravitational instantons are considered in this work as candidates for the description of multi-particle systems.