  This paper is devoted to the study of solitary waves and solitons whose
existence is related to the ratio energy/charge. These solitary waves are
called hylomorphic. This class includes the Q-balls, which are spherically
symmetric solutions of the nonlinear Klein-Gordon equation (NKG), as well as
solitary waves and vortices which occur, by the same mechanism, in the
nonlinear Schroedinger equation and in gauge theories. This paper is devoted to
the study of hylomorphic soliton. Mainly we will be interested in the very
general principles which are at the base of their existence such as the
Variational Principle, the Invariance Principle, the Noether theorem, the
Hamilton-Jacobi theory etc.
  We give a general definition of hylomorphic solitons and an interpretation of
their nature (swarm interpretation) which is very helpful in understanding
their behavior.
  We apply these ideas to the Nonlinear Schroedinger Equation (NS) and to the
Nonlinear Klein-Gordon Equation (NKG) repectively.
