Variational Methods in Nonlinear Field Theory

The book is divided in two parts. In the first part an abstract definition of solitary wave and soliton is given. Moreover an abstract theory for hylomorfic solitons, namely for those solitons which minimize the energy for a given charge, is developed. In the second part this theory is applied to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein- Gordon- Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equations...). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices.