Numerical computation of solitary wave solutions of the Rosenau equation

We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili meth...

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Bibliographic Details
Published in:Wave motion Vol. 98; p. 102618
Main Authors: Erbay, H.A., Erbay, S., Erkip, A.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.11.2020
Elsevier BV
Subjects:
Algorithms
Benjamin–Bona–Mahony equation
Iterative methods
Numerical analysis
Petviashvili iteration method
Robustness (mathematics)
Rosenau equation
Solitary waves
74J35
Petviashvili iteration method
Benjamin–Bona–Mahony equation
35Q53
65M99
74S30
Rosenau equation
Solitary waves
ISSN:0165-2125, 1878-433X
Online Access:Get full text
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Summary:We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations rely on a uniform discretization of a finite computational domain. Through some numerical experiments we observe that the algorithm converges rapidly and it is robust to very general forms of the initial guess. •A Petviashvili iteration method was used to solve the Rosenau equation numerically.•Solitary wave solutions were obtained for single and double power law nonlinearities.•Existence of the high-order dispersive term leads to the existence of non-monotonic tails.•The iteration scheme converges rapidly and it is robust to forms of initial guess.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2020.102618