کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1899847 1534065 2009 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conjugate Gradient method for finding fundamental solitary waves
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Conjugate Gradient method for finding fundamental solitary waves
چکیده انگلیسی

The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it can find fundamental solitary waves of nonlinear Hamiltonian equations. The main obstacle that such a modified CGM overcomes is that the operator of the equation linearized about a solitary wave is not sign definite. Instead, it has a finite number of eigenvalues on the opposite side of zero than the rest of its spectrum. We present versions of the modified CGM that can find solitary waves with prescribed values of either the propagation constant or power. We also extend these methods to handle multi-component nonlinear wave equations. Convergence conditions of the proposed methods are given, and their practical implications are discussed. We demonstrate that our modified CGMs converge much faster than, say, Petviashvili’s or similar methods, especially when the latter converge slowly.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 238, Issues 23–24, December 2009, Pages 2308–2330
نویسندگان
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