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\title{New and more dual-mode solitary wave solutions for the
Kraenkel-Manna-Merle system incorporating fractal effects}



\author[1]{Nauman Raza}%
\author[1]{Zara Hassan}%
\author[2]{Asma  Butt}%
\author[3]{Riaz  Rahman}%
\author[4]{Abdel-Haleem Abdel-Aty}%
\affil[1]{University of the Punjab}%
\affil[2]{UET}%
\affil[3]{Quaid-i-Azam University}%
\affil[4]{University of Bisha}%


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  \date{June 14, 2024}


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\begin{abstract}
This paper introduces the fractal Kraenkel-Manna-Merle (KMM) system,
that explains nonlinear short wave propagation with zero conductivity
for saturated ferromagnetic materials in an external field. The semi
inverse technique and the new auxiliary equation method (NAEM) are used
to generate a new set of solutions. The proposed methods are more
straightforward, succinct, accurate, and simple to calculate dual mode
solitary wave solutions. A collection of exact soliton solutions
specifically bright, dark, singular-shaped and singular-periodic are
generated. The estimated solutions are obtained using constraint
conditions and are displayed through 2D, 3D and contour plots with
appropriate parametric values. The arbitrary functions in the solutions
are chosen as unique functions to generate some novel soliton
structures.%
\end{abstract}%



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