Cubic–quartic optical solitons with Fokas–Lenells equation by the improved Adomian decomposition method

Abstract This article numerically examines the Fokas–Lenells equation with cubic-quartic dispersion, an integrable class member of complex-valued evolution equations that describes nonlinear pulse propagation in monomode optical media. Now, in solving the model, a new decomposition method, based on the original Adomian algorithm is adopted to construct the resulting recurrent scheme for the model. Moreover, to verify the exactness of the method, the study further seeks the help of the ansatz method to construct diverse exact solitary wave solutions for comparative analysis. At last, various error tables and comparison plots are reported, affirming the effectiveness of the adopted approach over existing methods in solving the cubic-quintic Fokas–Lenells equation, and by extension, the class of nonlinear complex-valued evolution equations.