Albert, John P.,Zeng, Lei.2013-08-162013-08-162000http://hdl.handle.net/11244/5980This 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.v, 51 leaves ;Solitons.Nonlinear functional analysis.Mathematics.Evolution equations, Nonlinear.Thesis