In this chapter, applying the qualitative theory of planar dynamical systems, we
study the traveling solitary wave solutions and loop solutions of several nonlinear evolution
equations. Dynamical behaviors and phase portraits are illustrated by numerical
simulations in differential parametric regions. Three typical traveling wave equations are
carefully investigated. All phase portraits of their corresponding traveling waves with
different profiles are given. Analysis from a theoretical viewpoint of dynamical systems
shows that the so-called loop- and inverted-loop-soliton solutions, as well as loop-periodic
solutions reportedly existing in the above three equations, are merely visual illusion of
numerical artifacts. To reveal the mystery, all the exact parametric representations of
traveling wave solutions of the above three equations are derived in precise analytical
forms.