Abstract
The complete discrimination system method is employed to find exact solutions for a dispersive cubic–quintic nonlinear Schrödinger equation with third order and fourth order time derivatives. As a result, we derive a range of solutions which include triangular function solutions, kink solitary wave solutions, dark solitary wave solutions, Jacobian elliptic function solutions, rational function solutions and implicit analytical solutions. Numerical simulations are presented to visualize the mechanism of Eq. (1) by selecting appropriate parameters of the solutions. The comparison between our results and other's works are also given.
Highlights
Propagation of short pulses in optical fibers is governed by the well-known nonlinear Schrodinger equation (NLS) [1]
Where E(z, t) is the slowly varying envelope of the electric field, β2 is the parameter of the group velocity dispersion, β3 and β4 are, respectively, the third-order and fourth-order dispersions, and γ1 and γ2 are the nonlinearity coefficients
The integrability of a nonlinear equation can be studied by applying the Painleve analysis
Summary
Propagation of short pulses in optical fibers is governed by the well-known nonlinear Schrodinger equation (NLS) [1]. The main purpose of this paper is to discuss the traveling wave solutions for a class of high dispersive cubic-Quintic nonlinear Schrodinger equations describing the ultrashort light pulse propagation as in the following: Ez. where E(z, t) is the slowly varying envelope of the electric field, β2 is the parameter of the group velocity dispersion, β3 and β4 are, respectively, the third-order and fourth-order dispersions, and γ1 and γ2 are the nonlinearity coefficients. Azzouzi et al [3] by using the extended hyperbolic auxiliary equation method in getting the exact explicit solutions to (1). He et al [4] find the exact bright, dark, and gray analytical nonautonomous soliton solutions of the generalized CQNLSE with spatially inhomogeneous group velocity dispersion (GVD) and amplification or attenuation by the similarity transformation method under certain parametric conditions.
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