應用Petviashvili方法求雙組份非線性薛丁格方程組的駐波解;The Numerical Approximation of Stationary Wave Solutions for Two-Component System of Nonlinear Schrodinger Equations by Using Generalization Petviashvili Method

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/75226

Title:	應用Petviashvili方法求雙組份非線性薛丁格方程組的駐波解;The Numerical Approximation of Stationary Wave Solutions for Two-Component System of Nonlinear Schrodinger Equations by Using Generalization Petviashvili Method
Authors:	諾斯拉 Robbaniyyah, Nuzla Af′idatur
Contributors:	國立中央大學
Keywords:	非线性薛定er方程;静止波;Nonlinear Schrodinger Equations;Stationary Wave;Petviashvili Method
Date:	2017-07-04
Issue Date:	2017-10-27 17:24:46 (UTC+8)
Abstract:	考慮這樣的穩態的非線性波動方程式：$Mu+u^p=0$，其中微分算子M是正定自伴算子，p是常數。只有一個方程式時，數值上一般可以用Petviashvili method求出孤立波解。此處我們的感興趣的問題是一些二維的雙組份非線性薛丁格方程組，我們將Petviashvili method推廣到此方程組，並得到數值上的收斂。; The Petviashvili method is a numerical method for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with-power-law nonlinearity: ?Mu + up = 0, where M is a positive de nite and self-adjoint operator, and p is constant. Due to the case is system of solitary nonlinear wave equations, we generalize the Petviashvili method. We apply this generalized method for two-component system of nonlinear Schrodinger equations (NLSE) for 2-D. From the numerical results, if the spectral radius of the numerical scheme for system is less than one, then we get quick convergence of the numerical method.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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