dc.contributor.author Bizoń, P dc.contributor.author Dunajski, M dc.contributor.author Kahl, M dc.contributor.author Kowalczyk, M dc.date.accessioned 2022-01-05T16:34:34Z dc.date.available 2022-01-05T16:34:34Z dc.date.issued 2021 dc.date.submitted 2020-12-23 dc.identifier.issn 0951-7715 dc.identifier.other nonac08eb dc.identifier.other ac08eb dc.identifier.other non-105060.r1 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/332099 dc.description.abstract In an attempt to understand the soliton resolution conjecture, we consider the Sine-Gordon equation on a spherically symmetric wormhole spacetime. We show that within each topological sector (indexed by a positive integer degree $n$) there exists a unique linearly stable soliton, which we call the $n$-kink. We give numerical evidence that the $n$-kink is a global attractor in the evolution of any smooth, finite energy solutions of degree $n$. When the radius of the wormhole throat $a$ is large enough, the convergence to the $n$-kink is shown to be governed by internal modes that slowly decay due to the resonant transfer of energy to radiation. We compute the exact asymptotics of this relaxation process for the $1$-kink using the Soffer-Weinstein weakly nonlinear perturbation theory. dc.language en dc.publisher IOP Publishing dc.subject Paper dc.subject soliton resolution conjecture dc.subject asymptotic stability of solitons dc.subject nonlinear dispersive equations dc.subject 35C08 dc.title Sine-Gordon on a wormhole dc.type Article dc.date.updated 2022-01-05T16:34:33Z prism.endingPage 5537 prism.issueIdentifier 8 prism.publicationName Nonlinearity prism.startingPage 5520 prism.volume 34 dc.identifier.doi 10.17863/CAM.79546 dcterms.dateAccepted 2021-06-07 rioxxterms.versionofrecord 10.1088/1361-6544/ac08eb rioxxterms.version VoR rioxxterms.licenseref.uri https://creativecommons.org/licenses/by/3.0/ dc.identifier.eissn 1361-6544 dc.publisher.url http://dx.doi.org/10.1088/1361-6544/ac08eb pubs.funder-project-id Science and Technology Facilities Council (ST/P000681/1) pubs.funder-project-id STFC (ST/T000694/1) cam.issuedOnline 2021-07-02
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