Optical solutions for a quintic derivative nonlinear Schrödinger equation using symmetry analysis

Abstract

In this paper, the derivative nonlinear Schrödinger equation with time-dependent-coefficient coefficients (DNLS) has been studied. This model is widely used in the hydrodynamic wave packets studies and optical fiber optics. The DNLS will be solved using a traveling wave transformation and Lie point symmetry analysis which is considered as a powerful tool that can be used in finding exact solutions of nonlinear partial differential equations (NLPDEs). The Lie symmetry technique provides a general way to obtain invariant solutions for NLPDEs. Some new exact solutions of the DNLS are obtained in the form of hyperbolic functions, Jacobi elliptic functions and Weierstrass elliptic function. The obtained waves have the forms of bright, dark and rogue waves soliton solutions which are considered as new solutions of the studied equation. The results established in this paper are new and extend the numbers of previously published results.