Traveling waves of a generalized sixth‐order Boussinesq equation

Amin Esfahani, Steven Levandosky

2024

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DOI 10.1002/mma.10067
Data confidence 70 medium
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Abstract

We investigate the existence and stability of traveling waves for the sixth‐order Boussinesq equation, considering a broad class of nonlinearities adhering to power‐like scaling relations. Employing the Nehari manifold method, we establish the existence of traveling waves and derive variational criteria for assessing their stability or instability. Subsequently, we develop a numerical approach based on these variational principles to delineate regions of stability and instability. Finally, for homogeneous nonlinearities, we establish a sufficient condition for strong instability.