Abstract
We address the existence and stability of fundamental solitons in a -symmetric Gaussian potential embedded into a material with fractional effects. Fundamental solitary waves with low power both in defocusing and focusing medium originate from the same eigenmode, and the smaller the Lévy index, the narrower the width of solitons. The linear stability analysis of fundamental solitons has been carried out in fractional dimension. -symmetric solitons are completely stable for a moderate Lévy index and gain/loss coefficient in a wide existence region.
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