The Linear KdV Equation with an Interface

Bernard Deconinck, Natalie E. Sheils, David A. Smith

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas’s Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.

Original languageEnglish (US)
Pages (from-to)489-509
Number of pages21
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Oct 1 2016

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