On the stability of solitary wave solutions for a generalized fractional Benjamin–Bona–Mahony equation

In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin–Bona–Mahony type equation. Besides the well known smooth and positive solitary wave with large wave speed, we present the existence of smooth negative solitary waves having small wave speed. The spectral stability is then determined by analysing the behaviour of the associated linearized operator around the wave …