On the variational structure of breather solutions II: periodic mKdV equation

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dc.contributor.authorAlejo, Miguel
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.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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent26 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAlejo, M. A., Muñoz, C., & Palacios, J. M. (2017). On the variational structure of breather solutions II: periodic mKdV equation. <i>Electronic Journal of Differential Equations, 2017</i>(56), pp. 1-26.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15582
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectModified KdV
dc.subjectSine-Gordon equations
dc.subjectPeriodic mKdV
dc.subjectIntegrability
dc.subjectBreather
dc.subjectStability
dc.titleOn the variational structure of breather solutions II: periodic mKdV equation
dc.typeArticle

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