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\begin{document}

\title{BINORMAL SCHRODINGER EVOLUTION OF WAVE POLARIZATION VECTOR OF LIGHT IN
THE NORMAL DIRECTION}



\author[1]{Talat Körpınar}%
\author[1]{Rıdvan Demirkol}%
\author[1]{Zeliha Körpınar}%
\author[2]{VEDAT ASİL}%
\affil[1]{Mus Alparslan Universitesi}%
\affil[2]{Firat Universitesi}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
In this paper, we mainly focus on the theory of evolution of wave
polarization in the normal direction of the curved path, which is
assumed to be the trajectory of the propagated light beam. The
polarization state of the wave is described by the unit complex
transverse field component by eliminating the longitudinal field
component, which reduces the dimension of the problem. A Coriolis term
is also effectively used to describe the relationship between the
geometric phase and the parallel transport law of the wave polarization
vector of the evolving light beam in the normal direction of the curved
path. We further present a unified geometric interpretation of the
binormal evolution of the wave polarization vector in the normal
direction of the curved path via the nonlinear Schrodinger equation of
repulsive type. Finally, we can sum up these discussions by
investigating the analytic solutions of the nonlinear Schrodinger
equation of repulsive type, which represents binormal evolution of the
polarization vector in the normal direction of the curved path
trajectory, for some special cases by using the traveling wave
hypothesis approach.%
\end{abstract}%



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