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Published in:
2018 | OriginalPaper | Chapter
The linearised Korteweg–deVries equation on general metric graphs
Author : Christian Seifert
Published in: The Diversity and Beauty of Applied Operator Theory
Publisher: Springer International Publishing
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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.