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dc.contributor.authorNixon, Sean D.
dc.contributor.authorYang, Jianke
dc.contributor.authorAkylas, Triantaphyllos R.
dc.date.accessioned2015-06-08T15:36:50Z
dc.date.available2015-06-08T15:36:50Z
dc.date.issued2013-03
dc.date.submitted2013-01
dc.identifier.issn00222526
dc.identifier.issn1467-9590
dc.identifier.urihttp://hdl.handle.net/1721.1/97216
dc.description.abstractAs a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multiscale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multiline-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.en_US
dc.description.sponsorshipUnited States. Air Force Office of Scientific Research (Grant USAF 9550-12-1-0244)en_US
dc.language.isoen_US
dc.publisherWiley Blackwellen_US
dc.relation.isversionofhttp://dx.doi.org/10.1111/sapm.12006en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleExponential Asymptotics for Line Solitons in Two-Dimensional Periodic Potentialsen_US
dc.typeArticleen_US
dc.identifier.citationNixon, Sean D., T. R. Akylas, and Jianke Yang. “Exponential Asymptotics for Line Solitons in Two-Dimensional Periodic Potentials.” Studies in Applied Mathematics 131, no. 2 (March 19, 2013): 149–178.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.mitauthorAkylas, Triantaphyllos R.en_US
dc.relation.journalStudies in Applied Mathematicsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsNixon, Sean D.; Akylas, T. R.; Yang, Jiankeen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5246-4574
mit.licenseOPEN_ACCESS_POLICYen_US


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