This paper uses the Hausdorff fractal derivative to convert the new Schrödinger nonlinear coupled equation into a novel fractal coupled nonlinear Schrödinger model. By applying the variational principle, a plethora of new soliton solutions are retrieved from the developed framework. The conditions of constraints are set for the presence of appropriate solitons. The 3D, 2D, and contour graphs of the reported solutions are depicted under the collection of appropriate parameter values. Moreover, it is noted that the variational principle built on the Hausdorff derivative for the proposed fractal model delivers a direct convenient and efficient mathematical tool for solving nonlinear partial differential equations in the solitary wave theory.

中文翻译：

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哈多夫分形新耦合非线性薛定谔模型及其新的孤波解

本文利用豪斯多夫分形导数将新的薛定谔非线性耦合方程转换为新的分形耦合非线性薛定谔模型。通过应用变分原理，从开发的框架中检索出大量新的孤子解决方案。约束条件是针对适当孤子的存在而设置的。报告的解决方案的 3D、2D 和等高线图在适当参数值的集合下进行了描述。此外，值得注意的是，所提出的分形模型基于 Hausdorff 导数的变分原理为求解孤立波理论中的非线性偏微分方程提供了一种直接方便且有效的数学工具。