Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method

Abstract

Abstract The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fractional perturbed Schrödinger’s equation with Kerr and parabolic law nonlinearity, and local conformable derivative. The method used in this article, called the generalized exponential rational function method, also relies heavily on the use of symbolic software such as Maple. The considered model has prominent applications in water optical metamaterials. The method retrieves several exponential, hyperbolic, and trigonometric function solutions to the model. The numerical evolution of the obtained solutions is also exhibited. The resulted wide range of solutions derived from the method proves its effectiveness in solving the model under investigation. It is also recommended to use the technique used in this article to solve similar problems.