Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data
Analysis of PDEs
2025-05-20 v1
Abstract
We show that solutions of the Korteweg-de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. The proof is based on a representation of reflectionless integrable potentials in terms of solutions to symmetric coupling problems for entire functions.
Cite
@article{arxiv.2311.01878,
title = {Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data},
author = {Jonathan Eckhardt},
journal= {arXiv preprint arXiv:2311.01878},
year = {2025}
}
Comments
11 pages