# The Linear KdV Equation with an Interface

@article{Deconinck2015TheLK,
title={The Linear KdV Equation with an Interface},
author={Bernard Deconinck and Natalie E. Sheils and David A. Smith},
journal={Communications in Mathematical Physics},
year={2015},
volume={347},
pages={489-509}
}
• Published 14 August 2015
• Mathematics
• Communications in Mathematical Physics
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…
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