The “good” Boussinesq equation : long-timeasymptotics

Abstract

We consider the initial-value problem for the "good" Boussinesq equation on the line.Using inverse scattering techniques, the solution can be expressed in terms of the solution of a 3 × 3-matrix Riemann-Hilbert problem.We establish formulas for the long-time asymptotics of the solution by performing a Deift-Zhou steepest descent analysis of a regularized version of this Riemann-Hilbert problem.Our results are valid for generic solitonless Schwartz class solutions whose space-average remains bounded as t → ∞.

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