  Regular Kadomtsev-Petviashvili II (KPII) line solitons have been investigated
and classified successfully by the Grassmannians. The inverse scattering method
provides a promising and powerful approach to study the stability properties of
$\textrm{Gr}(N, M)_{> 0}$ KP solitons. In this paper, we complete rigorous
analysis for the direct scattering problem of perturbed $\textrm{Gr}(N, M)_{>
0}$ KP solitons}.
