2008
DOI: 10.1103/physrevd.77.047701
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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

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Cited by 61 publications
(146 citation 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%
See 1 more Smart Citation
“…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%
“….. 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%
“…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%