From 1965 up to about 1975, a common agreement was reached: to reserve the term soliton to pulse-like solitary solutions of conservative nonlinear partial differential equations that can be solved by using the inverse scattering technique.
In contrast to conservative systems, solitons in fibers dissipate energy and this cannot be neglected on an intermediate and long time scale.
[10] There are however various types of systems which are capable of producing solitary structures and in which dissipation plays an essential role for their formation and stabilization.
Typical observations are (intrinsic) propagation, scattering, formation of bound states and clusters, drift in gradients, interpenetration, generation, and annihilation, as well as higher instabilities.
Up to now, modeling from first principles followed by a quantitative comparison of experiment and theory has been performed only rarely and sometimes also poses severe problems because of large discrepancies between microscopic and macroscopic time and space scales.
To understand and describe the latter, one may try to derive "particle equations" for slowly varying order parameters like position, velocity or amplitude of the DSs by adiabatically eliminating all fast variables in the field description.
This technique is known from linear systems, however mathematical problems arise from the nonlinear models due to a coupling of fast and slow modes.
[60][61] Note that the above problems do not arise for classical solitons as inverse scattering theory yields complete analytical solutions.