  A potential representation for the subset of traveling solutions of nonlinear
dispersive evolution equations is introduced. The procedure involves a
reduction of a third order partial differential equation to a first order
ordinary differential equation. In this representation it can be shown that
solitons and solutions with compact support only exist in systems with linear
or quadratic dispersion, respectively. In particular, this article deals with
so the called K(n,m) equations. It is shown that these equations can be
classified according to a simple point transformation. As a result, all
equations that allow for soliton solutions join the same equivalence class with
the Korteweg-deVries equation being its representative.
