Abstract
This paper aims to study the explicit fractional generalized nonlinear Schrödinger (fGNLS) equation by the Riemann–Hilbert (RH) method and to explore the impact of the order of fractional derivatives ϵ on solitons. Firstly, utilizing the recursion operator of the generalized nonlinear Schrödinger (GNLS) equation, the anomalous dispersion relation is constructed. Secondly, the explicit form of the fGNLS equation is obtained by the anomalous dispersion relation and the completeness. Then, the N-soliton solutions are acquired through RH problems. We found that the energy of the solitons decreases with the increase of the order of fractional derivatives ϵ. Specifically, we demonstrate that the fractional one-soliton solution constitutes a valid solution of the fGNLS equation by the Darboux transform.
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