New and more dual‐mode solitary wave solutions for the Kraenkel–Manna–Merle system incorporating fractal effects

Abstract

This paper introduces the fractal Kraenkel–Manna–Merle (KMM) system, which explains nonlinear short wave propagation with zero conductivity for saturated ferromagnetic materials in an external field. Fractal models deal with the discontinuous geometry of physical problems. The semi‐inverse technique and the new auxiliary equation method (NAEM) are used to generate a variety of solutions. A collection of exact soliton solutions specifically bright, dark, singular‐shaped, and singular‐periodic are generated using constraint conditions. The fractal parameter impact on these solutions displayed through 2D, 3D, and contour plots taking appropriate parametric values. The arbitrary functions in the solutions are chosen as such unique functions to generate some novel soliton structures. The proposed methods are more straightforward, succinct, and accurate to extract solitons of numerous evolution equations in mathematical physics.