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arXiv · 2303.10485

The soliton resolution conjecture for the Boussinesq equation

Christophe Charlier·Jonatan Lenells
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Abstract

We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main asymptotic sectors describing the large $(x,t)$-behavior of the solution, and for each of these sectors we provided the leading order asymptotics in the case when no solitons are present. In this paper, we give a formula valid in the asymptotic sector $x/t \in (1,M]$, where $M$ is a large positive constant, in the case when solitons are present. Combined with earlier results, this validates the soliton resolution conjecture for the Boussinesq equation everywhere in the $(x,t)$-plane except in a number of small transition zones.

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Christophe Charlier, Jonatan Lenells. 2023-03-18. The soliton resolution conjecture for the Boussinesq equation. https://arxiv.org/abs/2303.10485

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