應用Petviashvili方法求雙組份非線性薛丁格方程組的駐波解

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諾斯拉(Nuzla Af′idatur Robbaniyyah) 查詢紙本館藏

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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)

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摘要(中)

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。

摘要(英)

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 denite 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.

關鍵字(中)

★ 非线性薛定er方程
★ 静止波

關鍵字(英)

★ Nonlinear Schrodinger Equations
★ Stationary Wave
★ Petviashvili Method

論文目次

Contents
X i
Abstract ii
Acknowledgement iii
Contents iv
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Petviashvili Method . . . . . . . . . . . . . . . . . . . . . 3
2 Generalized Petviashvili Method and Its Convergence 6
2.1 Generalized Petviashvili Method for Single Equation . . 6
2.2 Generalized Petviashvili Method for System Equations . 10
2.3 Convergence of Numerical Scheme . . . . . . . . . . . . . 15
3 Numerical Computation Results and Discussion 18
3.1 Two-Component System of Nonlinear Schrodinger
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Two-Component System of Nonlinear Schrodinger
Equations with Epsilon Parameter (") . . . . . . . . . . . 22
4 Concluding Remarks 25
References 26

參考文獻

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27

指導教授

陳建隆(Jann-Long Chern)

審核日期

2017-7-4

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