Matches in SemOpenAlex for { <https://semopenalex.org/work/W4379964232> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W4379964232 abstract "We consider the sine-Gordon (SG) equation in 1+1 dimensions. The kink is a static, non-symmetric exact solution to SG, stable in the energy space $H^1times L^2$. It is well-known that the linearized operator around the kink has a simple kernel and no internal modes. However, it possesses an odd resonance at the bottom of the continuum spectrum, deeply related to the existence of the (in)famous wobbling kink, an explicit periodic-in-time solution of SG around the kink that contradicts the asymptotic stability of the kink in the energy space. In this paper, we further investigate the influence of resonances in the asymptotic stability question. We also discuss the relationship between breathers, wobbling kinks and resonances in the SG setting. By gathering Backlund transformations (BT) and Virial estimates around odd perturbations of the vacuum solution, we first identify the manifold of initial data around zero under which BTs are related to the wobbling kink solution. It turns out that (even) small breathers are deeply related to odd perturbations around the kink, including the wobbling kink itself. As a consequence of this result, using BTs we can construct a smooth manifold of initial data close to the kink, for which there is asymptotic stability in the energy space. The initial data has spatial symmetry of the form (kink + odd, even), non-resonant in principle, and not preserved by the flow. This asymptotic stability property holds despite the existence of wobbling kinks in SG. We also show that wobbling kinks are orbitally stable under odd data, and clarify some interesting connections between SG and $phi^4$ at the level of linear Backlund transformations." @default.
- W4379964232 created "2023-06-09" @default.
- W4379964232 creator A5006963626 @default.
- W4379964232 creator A5055086979 @default.
- W4379964232 creator A5071828958 @default.
- W4379964232 date "2020-03-20" @default.
- W4379964232 modified "2023-09-24" @default.
- W4379964232 title "On the asymptotic stability of the sine-Gordon kink in the energy space" @default.
- W4379964232 doi "https://doi.org/10.48550/arxiv.2003.09358" @default.
- W4379964232 hasPublicationYear "2020" @default.
- W4379964232 type Work @default.
- W4379964232 citedByCount "0" @default.
- W4379964232 crossrefType "posted-content" @default.
- W4379964232 hasAuthorship W4379964232A5006963626 @default.
- W4379964232 hasAuthorship W4379964232A5055086979 @default.
- W4379964232 hasAuthorship W4379964232A5071828958 @default.
- W4379964232 hasConcept C121332964 @default.
- W4379964232 hasConcept C127413603 @default.
- W4379964232 hasConcept C134306372 @default.
- W4379964232 hasConcept C138885662 @default.
- W4379964232 hasConcept C139210041 @default.
- W4379964232 hasConcept C158622935 @default.
- W4379964232 hasConcept C207821765 @default.
- W4379964232 hasConcept C2778572836 @default.
- W4379964232 hasConcept C33923547 @default.
- W4379964232 hasConcept C37914503 @default.
- W4379964232 hasConcept C41895202 @default.
- W4379964232 hasConcept C43466630 @default.
- W4379964232 hasConcept C44444269 @default.
- W4379964232 hasConcept C529865628 @default.
- W4379964232 hasConcept C62520636 @default.
- W4379964232 hasConcept C74455749 @default.
- W4379964232 hasConcept C74650414 @default.
- W4379964232 hasConcept C78519656 @default.
- W4379964232 hasConcept C87651913 @default.
- W4379964232 hasConceptScore W4379964232C121332964 @default.
- W4379964232 hasConceptScore W4379964232C127413603 @default.
- W4379964232 hasConceptScore W4379964232C134306372 @default.
- W4379964232 hasConceptScore W4379964232C138885662 @default.
- W4379964232 hasConceptScore W4379964232C139210041 @default.
- W4379964232 hasConceptScore W4379964232C158622935 @default.
- W4379964232 hasConceptScore W4379964232C207821765 @default.
- W4379964232 hasConceptScore W4379964232C2778572836 @default.
- W4379964232 hasConceptScore W4379964232C33923547 @default.
- W4379964232 hasConceptScore W4379964232C37914503 @default.
- W4379964232 hasConceptScore W4379964232C41895202 @default.
- W4379964232 hasConceptScore W4379964232C43466630 @default.
- W4379964232 hasConceptScore W4379964232C44444269 @default.
- W4379964232 hasConceptScore W4379964232C529865628 @default.
- W4379964232 hasConceptScore W4379964232C62520636 @default.
- W4379964232 hasConceptScore W4379964232C74455749 @default.
- W4379964232 hasConceptScore W4379964232C74650414 @default.
- W4379964232 hasConceptScore W4379964232C78519656 @default.
- W4379964232 hasConceptScore W4379964232C87651913 @default.
- W4379964232 hasLocation W43799642321 @default.
- W4379964232 hasOpenAccess W4379964232 @default.
- W4379964232 hasPrimaryLocation W43799642321 @default.
- W4379964232 hasRelatedWork W1980690149 @default.
- W4379964232 hasRelatedWork W1989975837 @default.
- W4379964232 hasRelatedWork W2025689585 @default.
- W4379964232 hasRelatedWork W2037046357 @default.
- W4379964232 hasRelatedWork W2040425488 @default.
- W4379964232 hasRelatedWork W2043718467 @default.
- W4379964232 hasRelatedWork W2338343474 @default.
- W4379964232 hasRelatedWork W3034897558 @default.
- W4379964232 hasRelatedWork W4220993915 @default.
- W4379964232 hasRelatedWork W174118584 @default.
- W4379964232 isParatext "false" @default.
- W4379964232 isRetracted "false" @default.
- W4379964232 workType "article" @default.