Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation

<p style='text-indent:20px;'>In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation is introduced, and its integrability as an infinite dimensional Hamilton dynamic system established. We successfully derive the inverse scattering transform (IST) of LPD equation. The direct problem first constructed, some important symmetries eigenfunctions data are discussed. By using novel Left-Right Riemann-Hilbert (RH) problem, analyzed, potential function recovered. introducing special conditions reflectionless case, time-periodic soliton solutions formula derived successfully. Take <inline-formula><tex-math id="M1">\begin{document}$ J = \overline{J} 1,2,3 $\end{document}</tex-math></inline-formula> id="M2">\begin{document}$ 4 for example, we obtain interesting phenomenon such breather-type solitons, arc three four soliton. Furthermore, influence parameter id="M3">\begin{document}$ \delta on these further considered via graphical analysis. Finally, eigenvalues conserved quantities investigated under few initial conditions.</p>