dc.contributor.author | Hildrum, Fredrik | |
dc.date.accessioned | 2020-02-20T16:08:56Z | |
dc.date.available | 2020-02-20T16:08:56Z | |
dc.date.created | 2020-02-17T18:03:15Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Nonlinearity. 2020, 33 (4), 1594-1624. | nb_NO |
dc.identifier.issn | 0951-7715 | |
dc.identifier.uri | http://hdl.handle.net/11250/2643081 | |
dc.description.abstract | We show existence of small solitary and periodic traveling-wave solutions in Sobolev spaces Hs, s>0, to a class of nonlinear, dispersive evolution equations of the formut+(Lu+n(u))x=0,where the dispersion L is a negative-order Fourier multiplier whose symbol is of KdV type at low frequencies and has integrable Fourier inverse K and the nonlinearity n is inhomogeneous, locally Lipschitz and of superlinear growth at the origin. This generalises earlier work by Ehrnström, Groves and Wahlén on a class of equations which includes Whitham’s model equation for surface gravity water waves featuring the exact linear dispersion relation. Tools involve constrained variational methods, Lions’ concentration-compactness principle, a strong fractional chain rule for composition operators of low relative regularity, and a cut-off argument for n which enables us to go below the typical s>12 regime. We also demonstrate that these solutions are either waves of elevation or waves of depression when K is nonnegative, and provide a nonexistence result when n is too strong. | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | IOP Publishing | nb_NO |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity | nb_NO |
dc.type | Journal article | nb_NO |
dc.type | Peer reviewed | nb_NO |
dc.description.version | publishedVersion | nb_NO |
dc.source.pagenumber | 1594-1624 | nb_NO |
dc.source.volume | 33 | nb_NO |
dc.source.journal | Nonlinearity | nb_NO |
dc.source.issue | 4 | nb_NO |
dc.identifier.doi | 10.1088/1361-6544/ab60d5 | |
dc.identifier.cristin | 1795002 | |
dc.relation.project | Norges forskningsråd: 250070 | nb_NO |
dc.description.localcode | Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. | nb_NO |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |