This study reveals some new solitons solutions to the Kraenkel–Manna–Merle (KMM) system which describes the nonlinear ultra-short wave pulse motions in saturated ferromagnetic materials having external field with zero-conductivity. Various kinds of soliton solutions such as dark, bright, singular, combined dark bright, combined dark-singular solitons, periodic and singular periodic waves are successfully constructed by applying two integration schemes, namely the extended sinh-Gordon equation expansion and the (\(\frac{G^{\prime }}{G^2}\)) expansion function methods. Thus, this study shows the effectiveness and simplicity of the proposed methods. The physical features of some reported solutions are portrayed via the 3D, 2D, and contour graphs under the choice of the suitable values of the parameters. The results reveal the system theoretically possesses extremely rich soliton structures.

这项研究揭示了Kraenkel–Manna–Merle（KMM）系统的一些新孤子解决方案，该解决方案描述了具有零电导率的外磁场的饱和铁磁材料中的非线性超短波脉冲运动。通过应用扩展的sinh-Gordon方程展开和（\（ \ frac {G ^ {\ prime}} {G ^ 2} \））扩展功能方法。因此，本研究表明了所提出方法的有效性和简便性。一些报道的溶液的物理特征的参数的适当值的选择下通过3D，2D，和轮廓的曲线图描绘。结果表明，该系统理论上具有极其丰富的孤子结构。