The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist.

中文翻译：

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具有幂律的 Fokas-Lenells 方程的三次-四次光学孤子微扰的半逆变分法

目前的工作解决了立方-四次孤子，以补偿作为孤子通过光纤传输的主要障碍之一的色散的低计数。因此，本文处理了控制跨洋和跨大陆距离的孤子通信的扰动 Fokas-Lenells 方程的三次-四次版本。该模型还考虑了非线性折射率的幂律形式，这是先前报道的结果的续集。这是对先前已知结果的巨大进步，该结果仅具有非线性折射率的克尔定律形式。本文主要通过将非线性克尔定律推广到非线性幂律来做出贡献。因此，先前的结果作为本文结果的一个特例而回落。半逆变分原理产生了一个明亮的 1 孤子解决方案，这对于电信工程师在橡胶接触道路之前进行实验研究是必不可少的。包括具有最大强度的哈密顿扰动项。孤子幅宽关系可以从任意次数的多项式方程中得到。参数约束也被识别为孤子存在。