0
Research Papers

Numerical Determination of Pseudobreathers of a Three-Dimensional Spherically Symmetric Wave Equation

[+] Author and Article Information
Janusz Karkowski

Faculty of Physics, Astronomy and
Applied Computer Science,
Marian Smoluchowski Institute of Physics,
Jagiellonian University,
Łojasiewicza 11,
Kraków 30-348, Poland
e-mail: januszk@th.if.uj.edu.pl

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 4, 2015; final manuscript received October 20, 2016; published online December 5, 2016. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 12(3), 031004 (Dec 05, 2016) (4 pages) Paper No: CND-15-1355; doi: 10.1115/1.4035193 History: Received November 04, 2015; Revised October 20, 2016

A numerical method for finding spherically symmetric pseudobreathers of a nonlinear wave equation is presented. The algorithm, based on pseudospectral methods, is applied to find quasi-periodic solutions with force terms being continuous approximations of the signum function. The obtained pseudobreathers slowly radiate energy and decay after some (usually long) time depending on the period that characterizes (unambiguously) the initial configuration.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Smiley, M. W. , 1990, “ Numerical Determination of Breathers and Forced Oscillations of Nonlinear Wave Equations,” Computational Solution of Nonlinear Systems of Equations (Lectures in Applied Mathematics), 3rd ed., Vol. 26, American Mathematical Society, Providence, RI, pp. 605–617.
Smiley, M. W. , 1989, “ Breathers and Forced Oscillations of Nonlinear Wave Equations on R3,” J. Reine Angew. Math., 1989(398), pp. 25–35.
Smiley, M. W. , 1988, “ Time-Periodic Solutions of Wave Equations on R1 and R3,” Math. Methods Appl. Sci., 10(4), pp. 457–475. [CrossRef]
Smiley, M. W. , 1992, “ On the Existence of Smooth Breathers for Nonlinear Wave Equations,” J. Differ. Equations, 96(2), pp. 295–317. [CrossRef]
Fodor, G. , Forgacs, P. , Grandclement, P. , and Rácz, I. , 2006, “ Oscillons and Quasibreathers in the phi(4) Klein-Gordon Model,” Phys. Rev. D, 74(12), p. 124003. [CrossRef]
Salmi, P. , and Hindmarsh, M. , 2012, “ Radiation and Relaxation of Oscillons,” Phys. Rev. D, 85(8), p. 085033. [CrossRef]
Arodź, H. , Klimas, P. , and Tyranowski, T. , 2008, “ Compact Oscillons in the Signum-Gordon Model,” Phys. Rev. D, 77(4), p. 047701. [CrossRef]
Arodź, H. , and Świerczynski, Z. , 2011, “ Swaying Oscillons in the Signum-Gordon Model,” Phys. Rev. D, 84(6), p. 067701. [CrossRef]
Arodź, H. , Karkowski, J. , and Świerczynski, Z. , 2013, “ Total Screening and Finite Range Forces From Ultramassive Scalar Fields,” Phys. Rev. D, 87(12), p. 125004. [CrossRef]
Boyd, J. P. , 2001, Chebyshev and Fourier Spectral Methods, Dover Publications, Mineola, NY.
Fornberg, B. , 1996, A Practical Guide to Pseudospectral Methods, Cambridge University Press, New York.
Gupta, A. , 2007, “ A Shared- and Distributed-Memory Parallel General Sparse Direct Solver,” AAECC, 18(3), pp. 263–277.
Segur, H. , and Kruskal, M. D. , 1987, “ Nonexistence of Small-Amplitude Breather Solutions in phi(4) Theory,” Phys. Rev. Lett., 58(8), pp. 747–750. [CrossRef] [PubMed]
Kichenassamy, S. , 1991, “ Breather Solutions of the Nonlinear Wave Equation,” Commun. Pure Appl. Math., 44(7), pp. 789–818. [CrossRef]
Denzler, J. , 1993, “ Nonpersistence of Breather Families for the Perturbed Sine Gordon Equation,” Common. Math. Phys., 158(2), pp. 397–430. [CrossRef]
Denzler, J. , 1995, “ Second Order Nonpersistence of the Sine Gordon Breather Under an Exceptional Perturbation,” Ann. Inst. Henri Poincaré Anal. Non Linéaire, 12(2), pp. 201–239. https://eudml.org/doc/78358

Figures

Grahic Jump Location
Fig. 1

Initial data: the function ψ(t=0,r) for T = 6.4

Grahic Jump Location
Fig. 2

Initial data: the function ψt(t=0,r) for T = 6.4

Grahic Jump Location
Fig. 3

Energy versus period T for different force terms

Grahic Jump Location
Fig. 4

Energy versus time for atan force and different T

Grahic Jump Location
Fig. 5

Energy versus time for erf force and different T

Grahic Jump Location
Fig. 6

Energy versus time for sqrt force and different T

Grahic Jump Location
Fig. 7

Energy versus time for tanh force and different T

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In