Oscillation rogue waves for the Kraenkel–Manna–Merle system in ferrites

Abstract

In this work, new analytical rogue wave solutions are first derived for the Kraenkel–Manna–Merle (KMM) system in ferrites by the truncated Painlevé method. Two free functions, which are respectively space and time variables, are involved in the solutions, and can be utilized to generate certain perturbations to the rogue waves. As the two functions are taken as trigonometric cosine functions, the novel periodic oscillation rogue waves can be observed. Further, it is found that the amplitude and frequency parameters of these cosine functions play crucial roles during the oscillation. The rogue waves can be separated into two symmetric ones by adjusting the amplitude parameter, while the rogue waves can be divided into many peaks and troughs by changing frequency parameter. Besides, both the amplitude and frequency parameters are also highly sensitive to the amplitude of the oscillation rogue waves. A series of figures and data are illustrated these new features.