Publication:
Collapse for the Higher-order Nonlinear Schrödinger Equation

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dc.contributor.authorAchilleos, V.
dc.contributor.authorDiamantidis, S.
dc.contributor.authorFrantzeskakis, D. J.
dc.contributor.authorHorikis, T. P.
dc.contributor.authorKarachalios, N. I.
dc.contributor.authorKevrekidis, P. G.
dc.contributor.departmentUniversity of Athens
dc.contributor.departmentUniversity of the Aegean
dc.contributor.departmentUniversity of Athens
dc.contributor.departmentUniversity of Ioannina
dc.contributor.departmentUniversity of the Aegean
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2023-09-23T14:43:58.000
dc.date.accessioned2024-04-26T18:38:59Z
dc.date.available2024-04-26T18:38:59Z
dc.date.issued2016-01-01
dc.description<p>Arxiv preprint uploaded. <a href="http://dx.doi.org/10.1016/j.physd.2015.11.005" id="x-ddDoi">doi:10.1016/j.physd.2015.11.005</a></p>
dc.description.abstractWe examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrödinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.
dc.description.pages57-68
dc.identifier.urihttps://hdl.handle.net/20.500.14394/34284
dc.relation.ispartofPhysica D
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=2235&amp;context=math_faculty_pubs&amp;unstamped=1
dc.source.issue316
dc.source.statuspublished
dc.subjectCollapse
dc.subjectinstabilities
dc.subjectsolitons
dc.subjectnonlinear optics
dc.subjectMathematics
dc.titleCollapse for the Higher-order Nonlinear Schrödinger Equation
dc.typearticle
dc.typearticle
digcom.contributor.authorAchilleos, V.
digcom.contributor.authorDiamantidis, S.
digcom.contributor.authorFrantzeskakis, D. J.
digcom.contributor.authorHorikis, T. P.
digcom.contributor.authorKarachalios, N. I.
digcom.contributor.authorKevrekidis, P. G.
digcom.identifiermath_faculty_pubs/1230
digcom.identifier.contextkey8265848
digcom.identifier.submissionpathmath_faculty_pubs/1230
dspace.entity.typePublication
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