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

Abstract

This thesis studies the existence and stability of solitary-wave solutions fx-ct of equations of the form ut+fux +Mut=0 . It is proved that there exist stable sets of solitary wave profile functions for a general class of equations of the above form. It is also found that, for the generalized Benjamin-Bona-Mahony equation, there are solitary wave profile functions that are not the minimizers of the associated variational problem.