{"title":"Approximate Solution to Non-Linear Schr\u00f6dinger Equation with Harmonic Oscillator by Elzaki Decomposition Method","authors":"Emad K. Jaradat, Ala\u2019a Al-Faqih","volume":146,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":30,"pagesEnd":34,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10010018","abstract":"

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.<\/p>\r\n","references":"\tRawashdeh M. S. and Maitama S. Solving coupled system of nonlinear PDEs using the Natural decomposition method, Int J Pure Appl Math, 92(2014) 757-776.\r\n\tNuruddeen R. I. and Nass A. M, Aboodh decomposition method and its application in solving linear and nonlinear heat equations, European Journal of Advances in Engineering and Technology, 3(7)(2016) 34-37.\r\n\tKhuri SA. A Laplace decomposition algorithm applied to a class of nonlinear deferential equations. Journal of Applied Mathematics.2001;1(4):141-155. \r\n\tEmad K. Jaradat WA Amer D Aloqali. Using Laplace Decomposition Method to Solve Non-linear Klein- Gordon Equation. UPB Sci Bull.2018;80(2): Series D.\r\n\tNuruddeen RI. Elzaki decomposition method and its applications in solving linear and nonlinear Schrodinger equations. Sohag Journal of Mathematics.2017; 4(2):1-5.\r\n\tAdomain G. Solution of physical problem by decomposition, Computers & Mathematics with Applications.1994; 27(9-10):145-154.\r\n\tAdomain G. A review of the decomposition method in applied mathematics. Journal of mathematical analysis and applications. 1988;135(2):501-544. \r\n\tBiazar, J., et al.\u201d Solution of the linear and non-linear Schr\u00f6dinger equations using homotopy perturbation and Adomain Decomposition methods.\u201d International Mathematical Forum. Vol.3. No.38. 2008.\r\n\tElzaki T. M., The new integral transform \u201c Elzaki Transform\u201d ,Global Journal of Pure and Applied Mathematics, 7(1)(2011) 57-64.\r\n\tZheng L, Wang T, Zhang X, Na L. The nonlinear Schr\u00f6dinger harmonic oscillator problem with small odd or even disturbances. Applied Mathematics Letters. 2013; 26(4):463-468.\r\n\tCresser J. Quantum Physics Notes. Department of Physics, Macquarie University, Australia.\r\n\tGriffiths DJ, Schroeter DF. Introduction to quantum mechanics. Cambridge University Press; 2018.\r\n\tTariq M. Elzaki, The New Integral Transform \u201c Elzaki Transform\u201d Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1(2011),PP.57-64.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 146, 2019"}