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arXiv · 2606.27690

Asymptotic stability for monotone traveling kinks of the dissipative Boussinesq problem

Atanas G. Stefanov
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Abstract

We study the dissipative Boussinesq problem, which extends the "good" Boussinesq equation by incorporating viscosity effects. It is well-known that this model supports monotone decreasing traveling kink solutions. We show that these kinks are orbitally stable in $H^1(\rone)$. Moreover, they are asymptotically stable in $\dot{H}^1(\rone)$ and $L^p(\rone), 2<p\leq \infty$.

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Atanas G. Stefanov. 2026-06-26. Asymptotic stability for monotone traveling kinks of the dissipative Boussinesq problem. https://arxiv.org/abs/2606.27690

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