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The Linear KdV Equation with an Interface

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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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Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA

    Bernard Deconinck

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Natalie E. Sheils

  3. Division of Science, Yale-NUS College, Singapore, 138527, Singapore

    David A. Smith

Authors
  1. Bernard Deconinck
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  2. Natalie E. Sheils
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  3. David A. Smith
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Correspondence to Natalie E. Sheils.

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Communicated by P. Deift

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Deconinck, B., Sheils, N.E. & Smith, D.A. The Linear KdV Equation with an Interface. Commun. Math. Phys. 347, 489–509 (2016). https://doi.org/10.1007/s00220-016-2690-z

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  • DOI: https://doi.org/10.1007/s00220-016-2690-z

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