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 socalled “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 manybody problems
(including those underlying the foundations of
statistical mechanics and thermodynamics).
