New single traveling wave solution in birefringent fibers or crossing sea waves on the high seas for the coupled Fokas–Lenells system

Abstract

The main work of this paper is focused on construction the single traveling wave solution of the coupled Fokas–Lenells system, which is usually used to simulate the propagation of ultrashort optical pulses in birefringent fibers or crossing sea waves on the high seas. Firstly, the coupled Fokas–Lenells system is simplified into a nonlinear ordinary differential equation by traveling wave transformation and linear transformation. Then, using the well-known complete discriminant system of third-order polynomials, some single traveling wave solutions of the coupled Fokas–Lenells system are obtained including implicit solutions, rational function solutions and Jacobian function solutions.

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