This paper introduces the fractal version of the higher-order dispersion model for the construction of novel soliton solutions through fractal variational technology. Higher-order dispersion model theoretical study of the soliton propagation dynamics is known in the absence of self-phase modulation. In the context of negligibly small group velocity dispersion, this model involves higher-order spatio-temporal dispersion and can be a core component of the telecommunications industry. Using the variational approach, the model effectively produces bright and dark soliton solutions. Essential novel conditions guaranteeing the existence of suitable solitons have been developed. The 3D, 2D and contour graphs of the computed effects are seen in the collection of the relevant parameter values. This study shows the significance and immense latency of variational technologies to the derivative nonlinear Schrödinger equation (DNLSE).

中文翻译：

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物理过程领域中出现的分形高阶色散模型及其分形变分原理

本文介绍了高阶色散模型的分形版本，用于通过分形变分技术构建新的孤子解。在没有自相位调制的情况下，孤子传播动力学的高阶色散模型理论研究是已知的。在群速度色散可忽略不计的情况下，该模型涉及高阶时空色散，可以成为电信行业的核心组成部分。使用变分方法，该模型有效地产生了明亮和黑暗的孤子解决方案。已经开发了保证合适孤子存在的基本新条件。在相关参数值的集合中可以看到计算效果的 3D、2D 和等高线图。