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We show how the inverse scattering transform can be used as a convenient toolto derive the long-time asymptotics of shock waves for the Korteweg-de Vries(KdV) equation in the soliton region. In particular, we improve the resultspreviously obtained via the nonlinear steepest decent approach both withrespect to the decay of the initial conditions as well as the region where theyare valid.

Soliton asymptotics for KdV shock waves via classical inverse scattering