Jacobi elliptic solutions, solitons and other solutions for the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity

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Why is it important?

Based on several integration tools, namely the Riccati equation method, the Bernoulli equation method, the extended auxiliary equation method, the new mapping method and the ϕ6ϕ6 -model expansion method, we obtain many exact solutions including the optical bright-dark-singular soliton solutions, Jacobi elliptic solutions and trigonometric function solutions of the nonlinear Schrödinger equation (NLSE) with fourth-order dispersion and cubic-quintic nonlinearity, self-steeping and self-frequency shift effects which describes the propagation of an optical pulse in optical fibers.