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2007, Volume 7, Issue 3: 465-495. Doi: 10.3934/dcdsb.2007.7.465
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Comparison of quarter-plane and two-point boundary value problems: The KdV-equation

  • 1.

    Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607

  • 2.

    Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, 38152

  • 3.

    Department of Mathematics, Virginia Tech, Blacksburg, VA 24061

  • 4.

    Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025

Received:  October 2006
Revised:  January 2007
Published:  May 2007
Abstract / Introduction Related Papers Cited by
    Abstract
  • This paper is concerned with the Korteweg-de Vries equation which models unidirectional propagation of small amplitude long waves in dispersive media. The two-point boundary value problem wherein the wave motion is specified at both ends of a finite stretch of length $L$ of the media of propagation is considered. It is shown that the solution of the two-point boundary value problem converges as $L\rightarrow +\infty$ to the solution of the quarter-plane boundary value problem in which a semi-infinite stretch of the medium is disturbed at its finite end. In addition to its intrinsic interest, our result provides justification for the use of the two-point boundary value problem in numerical studies of the quarter plane problem for the KdV equation.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 76B03.

    Citation:
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