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

Advances in Difference Equations

article

Ghanbari, Behzad¹  Nisar, Kottakkaran Sooppy³  Aldhaifallah, Mujahed⁴ 

[1] Department of Engineering Science, Kermanshah University of Technology;Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahçeşehir University;Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University;Systems Engineering Department, King Fahd University of Petroleum and Minerals

关键词: GERFM;    Wave solutions to PDEs;    Fractional operators;    Perturbed nonlinear Schrödinger’s equation;    Symbolic manipulation;    Nonlinearity laws;   

DOI  :  10.1186/s13662-020-02787-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY