Classical nonlinear optical waves propagating in multimode fibers typically exhibit complex interference patterns due to mode interactions. Under high optical power input, however, a distinctive phenomenon known as beam self-cleaning (BSC) emerges, characterized by the spontaneous redistribution of the optical power into the fiber's fundamental mode, resulting in a stable, Gaussian-like beam profile at the output. This study analyzes modal dynamics in graded-index multimode fibers, highlighting the robustness of BSC against perturbations such as fiber bending. Our results reveal that quasiresonance conditions among propagation constants effectively sustain BSC, even when strict four-wave mixing resonance conditions are disrupted. The analysis further suggests employing fibers with a larger refractive index difference as a practical strategy to enhance BSC robustness. Additionally, simulations incorporating Gaussian random variables in propagation constants confirm that the perturbations described by the corrections have a limited impact on the equilibrium mode occupancy distribution. These findings shed light on the mechanisms underpinning the persistence of BSC under realistic perturbations, providing guidelines for optimizing multimode fiber performance in high-power lasers and optical communication systems.

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• Nonlinear optics
• Nonlinear waveguides
• Turbulent mixing
• Waveguides