Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data

Jonathan Eckhardt

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arXiv · 2311.01878

Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data

Jonathan Eckhardt

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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.

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Jonathan Eckhardt. 2023-11-03. Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data. https://arxiv.org/abs/2311.01878

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