The direct scattering problem for the perturbed $\text{Gr}(1,2{)}_{\ge 0}$ Kadomtsev-Petviashvili solitons

Regular Kadomtsev-Petviashvili (KP) solitons have been investigated and classified successfully by the Grassmannian. We provide rigorous analysis for the direct scattering problem of perturbed $\text{Gr}(1,2{)}_{\ge 0}$ KP solitons.