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\begin{document}

\title{Exact and numerical solutions for the nano-soliton of ionic waves
propagating through microtubules in living cells}



\author[1]{Ahmet Bekir}%
\author[2]{Emad Zahran}%
\affil[1]{Eskisehir}%
\affil[2]{Benha University}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
In this article, the Paul-Painleve approach (PPA) which discovered
recently and built on the balance role has been used perfectly to
achieve new impressive solitary wave solutions to the nano-soliton of
ionic waves (NSOIW) propagating along microtubules in living cells. In
addition, the variational iteration method (VIM) has been applied in the
same vein and parallel to establish the numerical solutions of this
model.%
\end{abstract}%



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