Abstract
The concern of this paper is to explore the novel application of the first integral method and the modified (G′G2)-expansion method to determine the exact traveling wave solutions of the Fokas–Lenells equation. Three categories of exact solitary wave solutions, hyperbolic, trigonometric and rational solutions of the related equation are described with some free parameters. Complex transformation is adopted to convert the equation into ordinary differential equation which thusly resulted in abundant of new exact solutions.
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