Solution of (3 + 1)-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

Hassan A. Zedan; M. Ali Alghamdi

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Solution of (3 + 1)-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

机译：用微分变换法求解（3 +1）维非线性三次薛定inger方程

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Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.

机译：引入了四维差分变换方法，并首次定义了基本定理。此外，作为四维微分变换的应用，已经研究了偏微分方程非线性系统的精确解。将本方法的结果与系统的解析解进行了很好的比较。微分变换方法可以轻松地应用于线性或非线性问题，并减少了计算工作量。使用这种方法，无需繁琐的工作即可获得精确的解，并且它是用于解析和数值解的有用工具。

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《Mathematical Problems in Engineering》 |2012年第5期|p.12.1-12.14|共14页
作者
Hassan A. Zedan; M. Ali Alghamdi;
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Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia,Department of Mathematics, Faculty of Science, Kafr El-Sheikh University, Kafr El-Sheikh 33516, Egypt;

Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;

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机译：（1？+？1）维三次非线性Schrodinger方程新行波解的新颖（ G '/ G ）-扩展方法
2. A new general algebraic method with symbolic computation to construct new exact analytical solution for a (2+1)-dimensional cubic nonlinear Schrodinger equation [J] . Zheng Y, Zhang YY, Zhang HQ Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2007,第4期

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5. Bilinear Strichartz estimates in two dimensional compact manifolds and cubic nonlinear Schrodinger equations. [D] . Jiang, Jin-Cheng. 2009

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6. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations [O] . Brahim Benhammouda, Hector Vazquez-Leal -1

机译：微分变换方法的一种新的多步技术用于求解某些非线性可变时滞微分方程的解析解
7. Solution of (3+1)-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method [O] . Hassan A. Zedan, M. Ali Alghamdi 2012

机译：用差分变换法（3 + 1） - 二维非线性立方薛定甸方程的解决方案

Solution of (3 + 1)-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

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