On solitary waves for the Korteweg–de Vries equation on metric star graphs

Publikationstyp
Conference Paper
Date Issued
2023-07
Sprache
English
Author(s)
Mugnolo, Delio  
Noja, Diego  
Seifert, Christian  orcid-logo
Mathematik E-10  
TORE-URI
https://hdl.handle.net/11420/58379
First published in
Operator theory  
Number in series
307
Start Page
413
End Page
431
Citation
34th International Workshop on Operator Theory and is Applications, IWOTA 2023
Contribution to Conference
34th International Workshop on Operator Theory and is Applications IWOTA 2023  
Publisher DOI
10.1007/978-3-032-00155-9_18
Scopus ID
2-s2.0-105019312430
Publisher
Springer
We study the Korteweg–de Vries equation on a metric star graph and investigate existence of solitary waves on the metric graph in terms of the coefficients of the equation on each edge, the coupling condition at the central vertex of the star and the speeds of the travelling wave. We show that, with a continuity condition at the vertex, solitary waves can occur exactly when the parameters are chosen in a fairly special manner. We also consider coupling conditions beyond continuity.
DDC Class
510: Mathematics