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We consider the Boussinesq equation on the line for a broad class of Schwartzinitial data relevant for water waves. In a recent work, we identified ten mainsectors describing the asymptotic behavior of the solution, and for each ofthese sectors we gave an exact expression for the leading asymptotic term inthe case when no solitons are present. In this paper, we derive an asymptoticformula in Sector IV, characterized by $\frac{x}{t}\in (\frac{1}{\sqrt{3}},1)$,in the case when solitons are present. In particular, our results provide anexact expression for the soliton-radiation interaction to leading order and averification of the soliton resolution conjecture for the Boussinesq equationin Sector IV.

Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV