Abstract: Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a “real” loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions.

Key words: planar dynamical system, breaking wave solution, loop-solution, nonlinear