Exact and approximate solutions for a generalized form of the Schrödinger nonlinear equation

Subject Areas : Statistics

Behzad Ghanbari ¹ (Assistant Professor of Applied Mathematics, Department of Basic Sciences, Kermanshah University of Technology, Iran)

Received: 2019-04-13 Accepted : 2019-08-13 Published : 2020-12-21

Keywords: محاسبات نمادین, جواب‌های دقیق و عددی, معادله غیرخطی شرودینگر, معادلات با مشتقات جزئی, روش توابع نمایی کسری تعمیم یافته,

Abstract :

In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica. In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica.

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