论文标题
可集成的非本地Lakshmanan-Porsezian-Daniel方程的逆散射变换
Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation
论文作者
论文摘要
在这项工作中，引入了广义的非本地Lakshmanan-Porsezian-Daniel（LPD）方程，并建立了其作为无限维度汉密尔顿动态系统的整合性。由Ablowitz和Musslimani（2016年非线性29 915）的思想激励，我们成功地得出了非局部LPD方程的逆散射变换（IST）。方程的直接散射问题首先是构造的，并讨论了本征函数的一些重要对称性和散射数据。通过使用新型的左右Riemann-Hilbert（RH）问题，分析了反向散射问题，并恢复了电势函数。通过引入无反射情况的特殊条件，成功得出了方程的时间周期性孤子解决方案。以$ j = \ Overline {j} = 1,2,3 $和$ 4 $，例如，我们获得了一些有趣的现象，例如呼吸型孤子，弧形孤子，三个Soliton和四个Soliton。此外，通过图形分析进一步考虑了参数$δ$对这些溶液的影响。最后，在一些特殊的初始条件下研究了特征值和保守量。
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. Motivated by the ideas of Ablowitz and Musslimani (2016 Nonlinearity 29 915), 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 $J=\overline{J}=1,2,3$ and $4$ for example, we obtain some interesting phenomenon such as breather-type solitons, arc solitons, three soliton and four soliton. Furthermore, the influence of parameter $δ$ on these solutions is further considered via the graphical analysis. Finally, the eigenvalues and conserved quantities are investigated under a few special initial conditions.
