Diversity of exact solutions and solitary waves with the influence of damping effect in ferrites materials

The main concentration of this article is to investigate a series of abundant new soliton solutions to the ferrites materials. The Kraenkel-Manna-Merle (KMM) system is used as a governing model that expresses the nonlinear ultra-short wave pulse motions in ferrite’s materials having an external field with zero-conductivity. We extract the solutions in different forms like, Jacobi’s elliptic, hyperbolic, periodic, rational function solutions including a class of solitary wave solutions such that dark, singular, complex combo solitons, and mixed complex soliton solutions. Recently developed integration tool known as Φ6-model expansion method is applied to analyze the governing model. Moreover, the constraints conditions are explicitly presented for the resulting solutions and singular periodic wave solutions are recovered. Furthermore, for explaining the solutions in physical phenomena, the three dimensional and two dimensional graphs are plotted under the selection of appropriate parameters. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena. The findings indicate that the system has very rich soliton structures theoretically. •An integrable Kraenkel-Manna-Merle system is studied under zero damping effect in ferrites materials.•A new hydrodynamical Φ6-model expansion method is employed.•Exact solutions in the forms of Hyperbolic, dark, singular, periodic and combined soliton solutions are extracted.•Moreover, 3D and 2D profiles of some reported results with some suitable choice of parametric values have been depicted.