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

2023/11/03 by Eckhardt, Jonathan
#34L25 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 37K40 #Secondary 37K15

paper · doi:10.48550/arxiv.2311.01878

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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