Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Traveling wave solutions of a highly nonlinear shallow water equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2018 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 38, no 3, p. 1567-1604Article in journal (Refereed) Published
Abstract [en]

Motivated by the question whether higher-order nonlinear model equations, which go beyond the Camassa-Holm regime of moderate amplitude waves, could point us to new types of waves profiles, we study the traveling wave solutions of a quasilinear evolution equation which models the propagation of shallow water waves of large amplitude. The aim of this paper is a complete classification of its traveling wave solutions. Apart from symmetric smooth, peaked and cusped solitary and periodic traveling waves, whose existence is well-known for moderate amplitude equations like Camassa-Holm, we obtain entirely new types of singular traveling waves: periodic waves which exhibit singularities on both crests and troughs simultaneously, waves with asymmetric peaks, as well as multi-crested smooth and multi-peaked waves with decay. Our approach uses qualitative tools for dynamical systems and methods for integrable planar systems.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2018. Vol. 38, no 3, p. 1567-1604
Keywords [en]
Phase plane analysis, Shallow water equation, Traveling waves
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-222245DOI: 10.3934/dcds.2018065ISI: 000432845000025Scopus ID: 2-s2.0-85041085413OAI: oai:DiVA.org:kth-222245DiVA, id: diva2:1180305
Note

QC 20180205

Available from: 2018-02-05 Created: 2018-02-05 Last updated: 2018-06-19Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Quirchmayr, Ronald

Search in DiVA

By author/editor
Quirchmayr, Ronald
By organisation
Mathematics (Div.)
In the same journal
Discrete and Continuous Dynamical Systems
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 10 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf