Soliton asymptotics for the KdV shock problem of low regularity

in "From Complex Analysis to Operator Theory: A Panorama In Memory of Sergey Naboko", M. Brown (ed.) et al., Oper. Theory Adv. Appl., Birkhäuser, Basel (to appear).

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

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