Existence and breaking property of real loop-solutions of two nonlinear wave equations

Dynamical analysis has revealed that,for some nonlinear wave equations,loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loop-soliton 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" loop-solution exists,and if so,what are the precise parametric representations of these loop traveling wave solutions.