Communications in Mathematical Physics

, Volume 347, Issue 2, pp 489–509

The Linear KdV Equation with an Interface

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

DOI: 10.1007/s00220-016-2690-z

Cite this article as:
Deconinck, B., Sheils, N.E. & Smith, D.A. Commun. Math. Phys. (2016) 347: 489. doi:10.1007/s00220-016-2690-z


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.

Funding information

Funder NameGrant NumberFunding Note
National Science Foundation (US)
  • NSF-DGE-0718124

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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