非线性光学中Lakshmanan-Porsezian-Daniel方程的渐近分析

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-09-13 DOI:10.1016/j.wavemoti.2025.103633

Wentao Li , Zhao Zhang , Biao Li

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引用次数: 0

摘要

Lakshmanan-Porsezian-Daniel （LPD）方程描述了经典极限下双二次相互作用对海森堡双线性自旋链可积性的影响。利用多尺度方法，从LPD方程导出了Korteweg-de Vries （KdV）方程和广义的五阶KdV方程。基于摄动分析，构造了渐近单孤子解和双孤子解。KdV方程和广义五阶KdV方程中的色散项分别提供了孤子速度的一阶和高阶修正。通过对渐近单孤子解和双孤子解施加合适的周期边界条件，并应用傅里叶谱方法，得到了相应的数值解。数值结果与渐近解吻合较好，证实了所构造的LPD方程解的有效性。

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Asymptotic analysis on a Lakshmanan–Porsezian–Daniel equation in nonlinear optics

The Lakshmanan–Porsezian–Daniel (LPD) equation describes the effect of biquadratic interactions on the integrable properties of Heisenberg bilinear spin chains in the classical limit. By applying multiple-scale method, the Korteweg–de Vries (KdV) equation and a generalized fifth-order KdV equation are derived from the LPD equation. Based on the perturbation analysis, asymptotic one- and two-soliton solutions are constructed. The dispersive terms in the KdV and generalized fifth-order KdV equation provide the leading-order and higher-order corrections to the soliton velocities, respectively. Furthermore, the corresponding numerical solutions are obtained by imposing suitable periodic boundary conditions on the asymptotic one- and two-soliton solutions and applying the Fourier spectral method. The good agreement between the numerical results and the asymptotic solutions confirms the validity of the constructed solution for the LPD equation.

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.