Communications in Mathematical Physics

, Volume 347, Issue 2, pp 489–509 | Cite as

The Linear KdV Equation with an Interface

  • Bernard Deconinck
  • Natalie E. Sheils
  • David A. Smith
Article

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Bernard Deconinck
    • 1
  • Natalie E. Sheils
    • 2
  • David A. Smith
    • 3
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Division of ScienceYale-NUS CollegeSingaporeSingapore

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