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\begin{document}

\title{Dynamics of soliton solutions of the fifth-order nonlinear Schr\selectlanguage{ngerman}ödinger
equation via the Riemann-Hilbert approach\selectlanguage{english}}



\author[1]{Jin-Jie Yang}%
\author[1]{Shou-Fu Tian}%
\author[1]{TIan-Tian Zhang}%
\author[2]{Xiao-Li Wang}%
\affil[1]{China University of Mining and Technology}%
\affil[2]{Qilu University of Technology}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
The theory of inverse scattering is developed to investigate the
initial-value problem for the fifth-order nonlinear Schr\selectlanguage{ngerman}ödinger (foNLS)
equation under the zero boundary conditions at infinity. The spectral
analysis is performed in the direct scattering process, including the
establishment of the analytical, asymptotic and symmetric properties of
the scattering matrix and the Jost functions. In the inverse scattering
process, a suitable Riemann-Hilbert (RH) problem is successfully
established by using the modified eigenfunctions and scattering data,
and the relationship between the potential function and the solution of
the RH problem is successfully established. In order to further analyze
the propagation behavior of the solutions of the foNLS equation, we
present some new phenomena of studying the one-, two-, and three-
soliton solutions corresponding to simple zeros in scattered data.
Finally, we also analyze the one- and two-soliton solutions
corresponding to double zeros.%
\end{abstract}\selectlanguage{ngerman}%



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