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dc.contributor.authorAlejo, Miguel ( Orcid Icon 0000-0002-7104-3193 )
dc.contributor.authorMunoz, Claudio ( )
dc.contributor.authorPalacios, Jose ( )
dc.date.accessioned2022-03-31T13:08:33Z
dc.date.available2022-03-31T13:08:33Z
dc.date.issued2017-02-22
dc.identifier.citationAlejo, M. A., Muñoz, C., & Palacios, J. M. (2017). On the variational structure of breather solutions II: periodic mKdV equation. Electronic Journal of Differential Equations, 2017(56), pp. 1-26.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15582
dc.description.abstractWe study the periodic modified KdV equation, where a periodic in space and time breather solution is known from the work of Kevrekidis et al. [19]. We show that these breathers satisfy a suitable elliptic equation, and we also discuss via numerics its spectral stability. We also identify a source of nonlinear instability for the case described in [19], and we conjecture that, even if spectral stability is satisfied, nonlinear stability/instability depends only on the sign of a suitable discriminant function, a condition that is trivially satisfied in the case of non-periodic (in space) mKdV breathers. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.en_US
dc.formatText
dc.format.extent26 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectModified KdVen_US
dc.subjectSine-Gordon equationsen_US
dc.subjectPeriodic mKdVen_US
dc.subjectIntegrabilityen_US
dc.subjectBreatheren_US
dc.subjectStabilityen_US
dc.titleOn the variational structure of breather solutions II: periodic mKdV equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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