Abstract
The fourth-order dispersive nonlinear Schrödinger (FODNLS) equation can simulate the nonlinear propagation and interaction of ultrashort pulses in high-speed optical fiber transmission systems in optics. In this paper, all traveling wave solutions of the envelope are obtained by means of the polynomial complete discriminant system and the elementary integral method. Under specific parameters, the propagation modes of all solutions are given. In this paper, by using the direct integration method, all traveling wave solutions of the envelope of the equation are given, including the singular rational solution, the singular periodic solution, the solitary wave solution and the double periodic solution.
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