Résumé
I.The equation describing short waves dynamics on th surface of a fluid after a Green-Naghdi type reduction of Euler equations is found to be a new integrable system that exhibits very interesting properties. Indeed, an unexpected relation with the sine-Gordon model, through transformations involving a conserved quantity, leads to singular and multivalued solutions for the new equation and allows to build a description in terms of the Lagrangien of a relativistic field. The existence of cases very similar to this one leads us to investigate general condition for this kind of relations to appear and to study a model not explicitely Lorentz-invariant which mix two of the equations we obtained earlier.The last point we focus on is the effects on low-order quantum corrections due to those transformations. II. In order to find a consistent theory for higher-spin fields, we have studied a new way to build gauge groups and fields based on string field theory and mixing all levels of spin. We first calculate elements of the group and the composition law thanks to hermiticity constraints. We then choose the gauge fields to belong to the adjoint representation of the group and modify them to get closer to usual definitions. Eventually, the study of the spin 3 needs us to introduce auxiliary fields which can be used to build a Lagrangian for the massive spin 2, analogous to what Veltman did in the Yang-Mills case.