The nonlinear Schrödinger (NLS) equation is an ideal model for describing optical soliton transmission. This paper first introduces an integer-order generalized coupled NLS equation describing optical solitons in birefringence fibers. Secondly, the semi-inverse and fractional variational method is used to extend the integer‐order model to the space–time fractional order. Moreover, various nonlinear forms of fractional NLS equations are discussed, including the Kerr, power, parabolic, dual-power, and log law. The exact soliton solutions, such as bright, dark, and singular solitons, are given. Finally, the behavior of the solution is shown by three-dimensional figures with different fractional orders, which reveals the propagation characteristics of optical solitons in birefringence fibers described by the generalized coupled space–time fractional NLS equation.

中文翻译：

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双折射光纤中的光孤子与广义耦合时空分数阶非线性薛定谔方程

非线性薛定谔 (NLS) 方程是描述光孤子传输的理想模型。本文首先介绍了描述双折射光纤中光孤子的整数阶广义耦合 NLS 方程。其次，利用半逆和分数阶变分法将整数阶模型扩展到时空分数阶。此外，还讨论了分数阶 NLS 方程的各种非线性形式，包括克尔、幂、抛物线、双幂和对数定律。给出了精确的孤子解，例如亮孤子、暗孤子和奇异孤子。最后，解决方案的行为由具有不同分数阶的三维图形显示，