Compact oscillons in the signum-Gordon model

Arodź, Henryk; Klimas, P.; Tyranowski, T.

doi:10.1103/physrevd.77.047701

Cited by 59 publications

(146 citation statements)

References 8 publications

(7 reference statements)

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“…As we have already stressed several times, it is by now well understood that spatially localized breathers of the NLWE (2) do not exist in R D for general analytic potentials, even if a general mathematical proof is known only in D = 1. Let us note here, that a remarkable example in D = 1 admitting non-radiating breather-type solutions in the framework of "V "-shaped (non-differentiable) potentials evades this theorem [28]. In the case of analytic potentials, where the theorem applies there is still a point to be stressed.…”

Section: Higher Orders In the ε Expansionmentioning

confidence: 83%

“…[27] that the only non-trivial 1 + 1 dimensional scalar theory with real analytic self-interaction potential which admits breather solutions is the sine-Gordon (sG) theory. Interestingly in a recent work [28] a whole family non-radiating solutions of the 1 + 1 dimensional 'signum-Gordon' model has been found. This illustrates that one can expect new and surprising phenomena in theories where the interaction potential is not smooth.…”

Section: Introductionmentioning

confidence: 97%

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Small amplitude quasibreathers and oscillons

Fodor¹,

et al. 2008

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Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in D spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, Dcrit = 4, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

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Section: Higher Orders In the ε Expansionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 97%

Small amplitude quasibreathers and oscillons

Fodor¹,

et al. 2008

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“….. We then see that standard kinks and compact kinks appear from distinct Other studies revealed other possible routes to find compact solutions; see, e.g., Refs. [30][31][32][33][34][35]. In particular, in Ref.…”

Section: From Kinks To Compactonsmentioning

confidence: 99%

“…These structures are nontrivial configurations with compact support, and have been studied in distinct contexts in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In particular, in Ref.…”

Section: Introductionmentioning

confidence: 99%

High temperature effects on compact-like structures

Bazeia¹,

Lima²,

Losano³

2016

Eur. Phys. J. C

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In this work we investigate the transition from kinks to compactons at high temperatures. We deal with a family of models, described by a real scalar field with standard kinematics, controlled by a single parameter, real and positive. The family of models supports kink-like solutions, and the solutions tend to become compact when the parameter increases to larger and larger values. We study the oneloop corrections at finite temperature, to see how the thermal effects add to the effective potential. The results suggest that the symmetry is restored at very high temperatures.

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“…The present paper refers to recently investigated scalar field models with V-shaped potential [1]- [3]. Such potentials have a common feature -left-and right hand derivatives are different from zero at the minimum.…”

Section: Introductionmentioning

confidence: 99%

Perturbations of the signum-Gordon model

Klimas¹

2008

J. Phys. A: Math. Theor.

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We investigate a perturbation of a scalar field model (called here the signum-Gordon model) with the potential V (f ) = |f |. The perturbation generalizes the signum-Gordon model to the signum-Klein-Gordon model i.e. to the case V (f ) = |f | − 1 2 λf 2 , where λ is a small parameter. Such a generalization breaks the scaling symmetry of the signum-Gordon model. In this paper we concentrate on solutions for self-similar initial data. Such data are particulary useful for identification of the effects caused by the term that breaks the scaling symmetry. We have found that the behaviour of the solutions is quite interesting -they escape and return periodically to the selfsimilar initial data.

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Compact oscillons in the signum-Gordon model

Abstract: We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have a strictly finite size. They do not emit radiation.Comment: 12 pages, 4 figure

Cited by 59 publications

References 8 publications

Small amplitude quasibreathers and oscillons

Small amplitude quasibreathers and oscillons

High temperature effects on compact-like structures

Perturbations of the signum-Gordon model

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