The examination of the mutual influence of the two main trapping scenarios, which are characterized by B
and which in isolation yield the known
) and Gaussian (
) electron holes, show generalized, two-parametric solitary wave solutions. This increases the variety of hole solutions considerably beyond the two cases previously discussed, but at the expense of their mathematical disclosure, since
, the electrical wave potential, can no longer be expressed analytically by known functions. Therefore, they belong to a variety with a partially hidden mathematical background, a hitherto unexplored world of structure formation, the origin of which is the chaotic individual particle dynamics at resonance in the coherent wave particle interaction. A third trapping scenario
, being independent of (B, D) and representing the perturbative trapping scenarios in lowest order, provides a broad, continuous band of associated phase velocities
. For structures propagating near
, a Generalized Schamel equation is derived:
, which governs their evolution.
is associated with the phase speed and
are the renormalized time and electric potential, respectively, where
is the amplitude of the structure.