Under investigated in this paper is a Lakshmanan-Porsezian-Daniel equation that describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction or the propagation of the ultrashort pulses in a long-distance and high-speed optical fiber transmission system. Under certain parameter conditions, we simultaneously take the multi-pole phenomena and breather-to-soliton transitions into account, then utilize the second-order generalized Darboux transformation to derive the double-pole anti-dark solitons and graphically illustrate them. Asymptotic analysis is conducted to examine the interaction properties of double-pole anti-dark solitons, including their characteristic lines, amplitudes, phase shifts, slopes and position differences. Unlike the double-pole anti-dark solitons found in the Hirota equation, the ones in this study exhibit a distinct feature: Different soliton components share the same amplitude.

中文翻译：

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光纤或铁磁自旋链中 Lakshmanan-Porsezian-Daniel 方程的双极反暗孤子


本文研究的是 Lakshmanan-Porsezian-Daniel 方程，该方程描述了 （1+1） 维各向同性双二次海森堡铁磁自旋链中的非线性自旋激发，具有八极子-偶极子相互作用或超短脉冲在长距离高速光纤传输系统中的传播。在某些参数条件下，我们同时考虑多极点现象和呼吸层到孤子的转变，然后利用二阶广义 Darboux 变换来推导出双极点反暗孤子并以图形方式说明它们。进行渐近分析以检查双极反暗孤子的相互作用特性，包括它们的特征线、振幅、相移、斜率和位置差异。与 Hirota 方程中发现的双极反暗孤子不同，本研究中的孤子表现出一个明显的特征：不同的孤子分量具有相同的振幅。