research-article

A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity

Authors:

J. YangAuthors Info & Claims

Journal of Computational Physics, Volume 226, Issue 2

Pages 1668 - 1692

https://doi.org/10.1016/j.jcp.2007.06.009

Published: 01 October 2007 Publication History

Abstract

The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: -Mu+up=0, where M is a positive definite self-adjoint operator and p=const. In this paper, we propose a systematic generalization of this method to both scalar and vector Hamiltonian equations with arbitrary form of nonlinearity and potential functions. For scalar equations, our generalized method requires only slightly more computational effort than the original Petviashvili method.

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Cited By

Pasinlioğlu Ş(2024)Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equationsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02342-475:6Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s00033-024-02342-4
Yang K(2023)High Order Conservative Schemes for the Generalized Benjamin–Ono Equation on the Unbounded DomainJournal of Scientific Computing10.1007/s10915-023-02255-w96:2Online publication date: 15-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02255-w
Huang PYang Q(2022)Newton-Based Methods for Finding the Positive Ground State of Gross-Pitaevskii EquationsJournal of Scientific Computing10.1007/s10915-021-01711-990:1Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s10915-021-01711-9
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A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 226, Issue 2

October, 2007

1187 pages

ISSN:0021-9991

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 October 2007

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Cited By

Pasinlioğlu Ş(2024)Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equationsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02342-475:6Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s00033-024-02342-4
Yang K(2023)High Order Conservative Schemes for the Generalized Benjamin–Ono Equation on the Unbounded DomainJournal of Scientific Computing10.1007/s10915-023-02255-w96:2Online publication date: 15-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02255-w
Huang PYang Q(2022)Newton-Based Methods for Finding the Positive Ground State of Gross-Pitaevskii EquationsJournal of Scientific Computing10.1007/s10915-021-01711-990:1Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s10915-021-01711-9
Álvarez JDurán A(2016)Petviashvili type methods for traveling wave computationsMathematics and Computers in Simulation10.1016/j.matcom.2015.10.015123:C(19-36)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1016/j.matcom.2015.10.015
Dougalis VDurán AMitsotakis D(2016)Numerical approximation of solitary waves of the Benjamin equationMathematics and Computers in Simulation10.1016/j.matcom.2012.07.008127:C(56-79)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1016/j.matcom.2012.07.008
Lu JYing L(2016)Sparsifying preconditioner for soliton calculationsJournal of Computational Physics10.1016/j.jcp.2016.03.061315:C(458-466)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.03.061
Olson DShukla SSimpson GSpirn D(2016)Petviashvilli's Method for the Dirichlet ProblemJournal of Scientific Computing10.1007/s10915-015-0023-666:1(296-320)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1007/s10915-015-0023-6
Álvarez JDurán A(2014)Petviashvili type methods for traveling wave computationsJournal of Computational and Applied Mathematics10.1016/j.cam.2014.01.015266(39-51)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.1016/j.cam.2014.01.015
Chen PMalomed B(2012)Original articleMathematics and Computers in Simulation10.1016/j.matcom.2011.05.01382:6(1056-1068)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1016/j.matcom.2011.05.013
Álvarez JDurán A(2011)A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave modelsJournal of Computational and Applied Mathematics10.1016/j.cam.2010.07.015235:7(1790-1797)Online publication date: 1-Feb-2011
https://dl.acm.org/doi/10.1016/j.cam.2010.07.015
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