Steven Levandosky

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.