Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission.

光孤子是光纤在传播过程中波形和能量保持不变的物理现象，在信息传输中具有重要的应用价值。本文对描述不同频率光孤子传播的局部分数阶导数意义上的耦合非线性薛定谔方程进行了分析。获得了康托集上定义的不可微类型的精确行波解。讨论了固定分形维数特定解的特点。证明局部分数耦合非线性薛定谔方程可以描述光纤传输中分​​形波的相互作用。