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By employing a mapping to classical anharmonic oscillators, we explore aclass of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1dimensions and, by extension, asymptotically in general dimensions. We discussa possible way for creating approximate rogue wave like solutions to the NLSEby truncating exact solutions at their nodes and stitching them with othersolutions to the NLSE. The resulting waves are similar to compactons with thenotable difference that they are not localized but rather extend over all ofspace. We discuss rogue waves in a \phi^4 field theory in the context of adiscretized Lagrangian and rogue wave behavior is shown to evolve into a steadystate. Due to time-reversal invariance of this theory, the steady state foundcould alternatively evolve into a rogue wave giving rise to a large wave whichseems to appear from nothing.

Periodic Solutions and Rogue Wave Type Extended Compactons in the Nonlinear Schrodinger Equation and \phi^{4} Theories