Existence and stability of solitary-wave solutions of equations of Benjamin–Bona–Mahony type

We consider solitary-wave solutions of equations of Benjamin–Bona–Mahony type. We show that for a large class of equations of BBM type, there do exist stable sets consisting of solitary-wave profile functions. In the case of generalized BBM equations, we found that there are profile functions of stable solitary waves that are not the minimizers of the associated variational problem. Such a phenomenon is not known to exist for equations of Korteweg–de Vries type.