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.

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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



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