  The KdV equation can be derived in the shallow water limit of the Euler
equations. Over the last few decades, this equation has been extended to
include higher order effects. Although this equation has only one conservation
law, exact periodic and solitonic solutions exist. Khare and Saxena
\cite{KhSa,KhSa14,KhSa15} demonstrated the possibility of generating new exact
solutions by combining known ones for several fundamental equations (e.g.,
Korteweg - de Vries, Nonlinear Schr\"{o}dinger). Here we find that this
construction can be repeated for higher order, non-integrable extensions of
these equations. Contrary to many statements in the literature, there seems to
be no correlation between integrability and the number of nonlinear one
variable wave solutions.
