  In this report, fundamental educational concepts of linear and non-linear
equations and solutions of nonlinear equations from the book High-Temperature
Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer
Academic Publishers, Dordrecht, 2002, pages 101-142) is given. There are a few
ways to classify solitons. For example, there are topological and
nontopological solitons. Independently of the topological nature of solitons,
all solitons can be divided into two groups by taking into account their
profiles: permanent and timedependent. For example, kink solitons have a
permanent profile (in ideal systems), while all breathers have an internal
dynamics, even, if they are static. So, their shape oscillates in time. The
third way to classify the solitons is in accordance with nonlinear equations
which describe their evolution. Here we discuss common properties of solitons
on the basis of the four classification.
