Open AccessInverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation
Author(s) -
Weikang Xun,
ShouFu Tian,
Tiantian Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021259
Subject(s) - inverse scattering transform , inverse scattering problem , integrable system , soliton , mathematical physics , mathematics , inverse , breather , eigenvalues and eigenvectors , homogeneous space , scattering , riemann hypothesis , korteweg–de vries equation , mathematical analysis , physics , quantum mechanics , inverse problem , geometry , nonlinear system
In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation is introduced, and its integrability as an infinite dimensional Hamilton dynamic system is established. We successfully derive the inverse scattering transform (IST) of the nonlocal LPD equation. The direct scattering problem of the equation is first constructed, and some important symmetries of the eigenfunctions and the scattering data are discussed. By using a novel Left-Right Riemann-Hilbert (RH) problem, the inverse scattering problem is analyzed, and the potential function is recovered. By introducing the special conditions of reflectionless case, the time-periodic soliton solutions formula of the equation is derived successfully. Take \begin{document}$ J = \overline{J} = 1,2,3 $\end{document} and \begin{document}$ 4 $\end{document} for example, we obtain some interesting phenomenon such as breather-type solitons, arc solitons, three soliton and four soliton. Furthermore, the influence of parameter \begin{document}$ \delta $\end{document} on these solutions is further considered via the graphical analysis. Finally, the eigenvalues and conserved quantities are investigated under a few special initial conditions.