We investigate nonlinear phenomena
utilizing “exact” mathematical approaches,
within the context of the progress of the last decades
concerning “integrable” dynamical systems
with a number of degrees of freedom either finite
(i. e., systems of nonlinear ODEs) or infinite
(i.e., nonlinear PDEs):
the so-called “soliton revolution”.
In addition to findings the primary interest
of which is mathematical, our results are
relevant to nonlinear optics, to fluid dynamics,
and to classical many-body problems
(including those underlying the foundations of
statistical mechanics and thermodynamics).