  We give a classification of the $regular$ soliton solutions of the KP
hierarchy, referred to as the $KP solitons$, under the Gel'fand-Dickey
$\ell$-reductions in terms of the permutation of the symmetric group. As an
example, we show that the regular soliton solutions of the (good) Boussinesq
equation as the 3-reduction can have $at ~most$ one resonant soliton in
addition to two sets of solitons propagating in opposite directions. We also
give a systematic construction of these soliton solutions for the
$\ell$-reductions using the vertex operators. In particular, we show that the
$non-crossing$ permutation gives the regularity condition for the soliton
solutions.
