  Inequality width-amplitude relations for three-dimensional
Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas.
Criteria for neglecting effects of nonzero cyclotron radius are obtained. We
emphasize that the form of the solitary potential is not tightly constrained,
and the amplitude and widths of the potential are constrained by inequalities.
The existence of a continuous range of allowed sizes and shapes for these waves
makes them easily accessible. We propose that these solitary waves can be
spontaneously generated in turbulence or thermal fluctuations. We expect that
the high excitation probability of these waves should alter the bulk properties
of the plasma medium such as electrical resistivity and thermal conductivity.
