The Boussinesq equation on the half-line

Christophe Charlier

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arXiv · 2504.19663

The Boussinesq equation on the half-line

Christophe Charlier

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Abstract

We study the initial-boundary value problem for the Boussinesq equation on the half-line. Assuming that the solution exists, we prove that it can be recovered from its initial-boundary values via the solution of a $3\times 3$ Riemann-Hilbert problem. The contour consists of $18$ arcs on the unit circle, $18$ segments and $18$ half-lines, and the associated jump matrices involve $9$ reflection coefficients.

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Christophe Charlier. 2025-04-28. The Boussinesq equation on the half-line. https://arxiv.org/abs/2504.19663

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