The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part,the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part,the authorsapply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like theexistence of vortices. The books is addressed to Mathematicians and Physicists.
Table of Contents1The general principles.- 2Solitary waves and solitons: abstract theory.- 3The nonlinear Schrödinger equation.- 4The nonlinear Klein-Gordon equation.- 5The Nonlinear Klein-Gordon-Maxwell equations.- 6The nonlinear Schrödinger-Maxwell equations.- 7The nonlinear beam equation.- 8Vortices.- 9Appendix.