Soliton asymptotics for the KdV shock problem of low regularity

2022/02/17 by Iryna Egorova, Egorova, Iryna, Johanna Michor +3
Mathematics · Physics and Astronomy · #35Q15 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Primary 37K40 #Secondary 37K45 #math-ph #math.AP #math.MP #msc:35Q15 #msc:35Q53 #msc:37K40 #msc:37K45

paper · pdf · doi:10.48550/arxiv.2202.08507

18 pages

arxiv created 2022/02/17 · openalex publication_date 2022/02/17 · arxiv updated 2022/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the asymptotic analysis of the KdV shock problem in the soliton region. Our approach is based on the analysis of the associated Riemann-Hilbert problem and we extend the domain of validity of the asymptotic formulas while at the same time requiring less decay and smoothness for the initial data.

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