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arXiv · 2603.12370

Superposition of shock waves of the generalized BBM equation

Alexey Samokhin
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Abstract

The generalized BBM studied in this paper contains an additional dissipative term. Thus instead of solitons for the classic BBM there exists a lot of travelling shock wave solutions. The rules of their interactions or superposition is of high importance. The paper gives a detailed description of the two-parameter family of travelling wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable not exclusively to the travelling wave solutions of BBM, but also to a wider class of shock waves, in particular discontinuous. Characteristic examples are illustrated by numerically worked out graphs.

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Alexey Samokhin. 2026-03-12. Superposition of shock waves of the generalized BBM equation. https://arxiv.org/abs/2603.12370

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