The linearised Korteweg–deVries equation on general metric graphs

Publikationstyp
Book Part
Date Issued
2018
Sprache
English
Author(s)
Seifert, Christian  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/3457
First published in
Operator theory  
Number in series
268
Start Page
449
End Page
458
Citation
in: The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications (268) : 449-458 (2018)
Publisher DOI
10.1007/978-3-319-75996-8_25
Scopus ID
2-s2.0-85046262241
Publisher
Birkhäuser
We consider the linearised Korteweg–deVries equation, sometimes called Airy equation, on general metric graphs with edge lengths bounded away from zero. We show that properties of the induced dynamics can be obtained by studying boundary operators in the corresponding boundary space induced by the vertices of the graph. In particular, we characterise unitary dynamics and contractive dynamics. We demonstrate our results on various special graphs, including those recently treated in the literature.
Subjects
Generators of C -semigroups 0
Linearised KdV-equation
Metric graphs
DDC Class
000: Allgemeines, Wissenschaft