Applications of a Generalized Extended (G'/G) -Expansion Method to Find Exact Solutions of Two Nonlinear Schrödinger Equations with Variable Coefficients

Abstract

In the present paper, we construct the travelling wave solutions of two nonlinear Schrödinger equations with variable coecients by using a generalized extended-expansion method, where G = G(ξ) satises a second order linear ordinary dierential equation. By using this method, new exact solutions involving parameters, expressed by hyperbolic and trigonometric function solutions are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

“…The transmission of a soliton in the real communication system of an optical soliton is described by Eq. (1) [9].…”

“…Searching for exact solutions of these FDEs plays an important and significant role in the study on the dynamics of those phenomena. Many powerful methods have been proposed to handle this subject, such as the Darboux transformation method [6], the split-step Fourier transform method [7], the fractional characteristic method [8,9]. But because of the complexity of the nonlinear terms, most FDEs do not have exact analytic solutions, so approximate and numerical methods must be used.…”

On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients

“…In order to better understand these phenomena, it is important to search for exact solutions to these equations. A variety of methods for obtaining exact solutions of NLEEs have been presented [1–8] . However, to the best of our knowledge, most of the aforementioned methods were related to the constant coefficient models.…”