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

## TL;DR

This paper rigorously analyzes the direct scattering problem for perturbed KP solitons associated with the Grassmannian, extending understanding beyond regular solitons.

## Contribution

It provides the first rigorous analysis of the direct scattering problem for perturbed Grassmannian KP solitons, expanding the mathematical framework.

## Key findings

- Established the mathematical foundation for scattering of perturbed KP solitons
- Extended the classification of KP solitons to include perturbations
- Provided tools for future analysis of soliton stability and interactions

## Abstract

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 $\textrm{Gr}(1, 2)_{\ge 0}$ KP solitons.