# Real soliton lattices of KP-II and desingularization of spectral curves: the Gr^{TP}(2,4) case

## TL;DR

This paper constructs real finite-gap KP-II soliton lattices associated with smooth genus 4 M-curves, providing a geometric desingularization of reducible rational curves for specific soliton data.

## Contribution

It extends the construction of real KP-II solutions to the case of Gr^{TP}(2,4), introducing a geometric desingularization approach for spectral curves.

## Key findings

- Constructed finite-gap KP-II solutions as soliton lattices.
- Connected smooth genus 4 M-curves with reducible rational curves.
- Provided a geometric framework for spectral curve desingularization.

## Abstract

We apply the general construction developed in references [4,5] to the first non-trivial case of Gr^{TP}(2,4). In particular, we construct finite-gap KP-II real quasiperiodic solutions in the form of soliton lattice corresponding to a smooth genus 4 M-curve, which is a desingularization of a reducible rational M-curve for soliton data in Gr^{TP}(2,4).