Abstract
In this paper, a wide range of new exact solutions of the Kraenkel–Manna–Merle (KMM) system is investigated. To study this, we have considered two analytical methods namely the new sub-equation (NSE) method and modified Khater’s (mK) method. The obtained solutions result in distinct wave natures for different numerical parameters and in the presence and absence of a damping factor. These are anti-peakon, three-soliton propagation, mixed soliton-anti-kink, mixed two-soliton-anti-kink, two bright soliton propagation, anti-kink, a grey-type periodic wave, periodic, dark, bright, grey, bright periodic, u-shaped periodic and evolving wave shape solutions. Graphical representations are made in order to carefully examine and analyse these dynamical characteristics of the derived solutions. Additionally, these wave properties are very useful in explaining the behaviour of magnetic materials both in the absence and presence of damping factor. Furthermore, it can be helpful in discussing additional uses of magnetic materials in various aspects.