On the stability of solitary waves of a generalized Ostrovsky equation

We consider the stability of ground state solitary waves of the generalized Ostrovsky equation \(( u_t - \beta u_{xxx} + f(u)_x)_x = \gamma u\), with homogeneous nonlinearities of the form \(f(u)=a_e|u|^p+a_o|u|^{p-1}u\). We obtain bounds on the function \(d\) whose convexity determines the stability of the solitary waves. These bounds imply that, when \(2\le p 0\) small, solitary waves are stable when \(2\le p 5\). We also numerically compute the function \(d\), and thereby determine precise regions of stability and instability, for several nonlinearities.