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

Superposition solutions to the extended KdV equation for water surface waves