On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation

In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), Fourier pseudospectral method (FPSM), Crank-Nicolson method (CNM), and Hopscotch method (HSM), are exhaustively presented for solving the 1D nonlinear Schrodinger equation (NLSE). The significance o...

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Auteurs principaux:	Neveen G. A. Farag, Ahmed H. Eltanboly, M. S. EL-Azab, S. S. A. Obayya
Format:	article
Langue:	EN
Publié:	Hindawi Limited 2021
Sujets:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/b2c66e18033a4ceea69fee3371ac016a
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spelling	oai:doaj.org-article:b2c66e18033a4ceea69fee3371ac016a2021-11-15T01:20:05ZOn the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation1563-514710.1155/2021/3094011https://doaj.org/article/b2c66e18033a4ceea69fee3371ac016a2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3094011https://doaj.org/toc/1563-5147In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), Fourier pseudospectral method (FPSM), Crank-Nicolson method (CNM), and Hopscotch method (HSM), are exhaustively presented for solving the 1D nonlinear Schrodinger equation (NLSE). The significance of this equation is referred to its notable contribution in modeling wave propagation in a plethora of crucial real-life applications such as the fiber optics field. Although exact solutions can be obtained to solve this equation, these solutions are extremely insufficient because of their limitations to only a unique structure under some limited initial conditions. Therefore, seeking high-performance numerical techniques to manipulate this well-known equation is our fundamental purpose in this study. In this regard, extensive comparisons of the proposed numerical approaches, against the exact solution, are conducted to investigate the benefits of each of them along with their drawbacks, targeting a broad range of temporal and spatial values. Based on the obtained numerical simulations via MATLAB, we extrapolated that the SSFT invariably exhibits the topmost robust potentiality for solving this equation. However, the other suggested schemes are substantiated to be consistently accurate, but they might generate higher errors or even consume more processing time under certain conditions.Neveen G. A. FaragAhmed H. EltanbolyM. S. EL-AzabS. S. A. ObayyaHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Neveen G. A. Farag Ahmed H. Eltanboly M. S. EL-Azab S. S. A. Obayya On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
description	In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), Fourier pseudospectral method (FPSM), Crank-Nicolson method (CNM), and Hopscotch method (HSM), are exhaustively presented for solving the 1D nonlinear Schrodinger equation (NLSE). The significance of this equation is referred to its notable contribution in modeling wave propagation in a plethora of crucial real-life applications such as the fiber optics field. Although exact solutions can be obtained to solve this equation, these solutions are extremely insufficient because of their limitations to only a unique structure under some limited initial conditions. Therefore, seeking high-performance numerical techniques to manipulate this well-known equation is our fundamental purpose in this study. In this regard, extensive comparisons of the proposed numerical approaches, against the exact solution, are conducted to investigate the benefits of each of them along with their drawbacks, targeting a broad range of temporal and spatial values. Based on the obtained numerical simulations via MATLAB, we extrapolated that the SSFT invariably exhibits the topmost robust potentiality for solving this equation. However, the other suggested schemes are substantiated to be consistently accurate, but they might generate higher errors or even consume more processing time under certain conditions.
format	article
author	Neveen G. A. Farag Ahmed H. Eltanboly M. S. EL-Azab S. S. A. Obayya
author_facet	Neveen G. A. Farag Ahmed H. Eltanboly M. S. EL-Azab S. S. A. Obayya
author_sort	Neveen G. A. Farag
title	On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
title_short	On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
title_full	On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
title_fullStr	On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
title_full_unstemmed	On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation
title_sort	on the analytical and numerical solutions of the one-dimensional nonlinear schrodinger equation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/b2c66e18033a4ceea69fee3371ac016a
work_keys_str_mv	AT neveengafarag ontheanalyticalandnumericalsolutionsoftheonedimensionalnonlinearschrodingerequation AT ahmedheltanboly ontheanalyticalandnumericalsolutionsoftheonedimensionalnonlinearschrodingerequation AT mselazab ontheanalyticalandnumericalsolutionsoftheonedimensionalnonlinearschrodingerequation AT ssaobayya ontheanalyticalandnumericalsolutionsoftheonedimensionalnonlinearschrodingerequation
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On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation

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