Optical soliton solutions to the Fokas–Lenells equation via sine-Gordon expansion method and $$(m+({G'}/{G}))$$-expansion method

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The purpose of this study is to find some novel soliton solutions of Fokas–Lenells (FL) equation where the perturbation terms are taken into account with nonlinearity. The sine-Gordon expansion method (SGEM) and the $$(m+({G'}/{G}))$$ -expansion method are used in this context. The dark, bright, dark–bright and singular optical soliton solutions are successfully obtained. Moreover, the constraint conditions for guaranteeing the existence of solutions are also given.