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arXiv · 2605.19906

Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation

Xijun Deng·Stephane Lafortune·Zhisu Liu
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Abstract

The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow water waves capable of capturing wave steepening and breaking. Despite its similarities with integrable shallow-water equations, the FW equation is not completely integrable. Nevertheless, the FW equation is part of the family of peakon-type models as it supports peaked traveling wave solutions. In this paper, we consider smooth solitary wave solutions to the FW equation. We use a variational approach to show that some are orbitally stable.

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Xijun Deng, Stephane Lafortune, Zhisu Liu. 2026-05-19. Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation. https://arxiv.org/abs/2605.19906

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