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Soliton asymptotics for the KdV shock problem of low regularity

I. Egorova, J. Michor, and G. Teschl

Keywords: KdV equation, shock problem, nonlinear steepest descent, low regularity, solitons.

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.

MSC: Primary 37K40, 35Q53; Secondary 37K45, 35Q15.

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arXiv:2202.08507