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arXiv · 1508.03596

The Linear KdV Equation with an Interface

Bernard Deconinck·Natalie E. Sheils·David A. Smith
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Abstract

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.

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Bernard Deconinck, Natalie E. Sheils, David A. Smith. 2016-09-19. The Linear KdV Equation with an Interface. https://doi.org/10.1007/s00220-016-2690-z

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