Riemann–Hilbert approach, dark solitons and double‐pole solutions for Lakshmanan–Porsezian–Daniel equation in an optical fiber, a ferromagnetic spin or a protein

Su‐Su Chen, Bo Tian, He‐Yuan Tian, Cong-Cong Hu
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Abstract

Inverse scattering transform for the defocusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is constructed via the Riemann–Hilbert approach. Since poles of the associated reflection coefficient are simple, ‐dark soliton solutions corresponding to simple poles are constructed. For ‐dark soliton solutions, results show that the soliton amplitude and width are not affected by the strength of the higher‐order linear and nonlinear effects , but soliton velocity has a linear correlation with ; the interactions between the two‐dark solitons and among the three‐dark solitons are elastic and experience phase and position shifts. Besides, asymptotic analysis of the double‐pole solutions for the focusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is presented. Different from ‐dark soliton solutions which locate in the straight lines and experience position shift after the interaction, the double‐pole solutions diverge from each other logarithmically and experience no position shift after the interaction.
光纤、铁磁自旋或蛋白质中拉克希曼-波尔舍西安-丹尼尔方程的黎曼-希尔伯特方法、暗孤子和双极解决方案
通过黎曼-希尔伯特(Riemann-Hilbert)方法,构建了具有非零边界条件的失焦拉克什曼-波齐安-丹尼尔方程的反散射变换。由于相关反射系数的极点是简单的,因此构建了与简单极点相对应的-暗孤子解。对于-暗孤子解,结果表明孤子振幅和宽度不受高阶线性和非线性效应强度的影响,但孤子速度与之呈线性相关;二暗孤子之间以及三暗孤子之间的相互作用是弹性的,并经历相位和位置偏移。此外,还对具有非零边界条件的聚焦拉克什曼-波尔齐安-丹尼尔方程的双极解进行了渐近分析。与位于直线上并在相互作用后发生位置偏移的-暗孤子解不同,双极解在相互作用后对数发散且不发生位置偏移。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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