Computing the weak limit of KdV

David W. McLaughlin, John A. Strain

Research output: Contribution to journalArticlepeer-review


The solution of the KdV equation with single‐minimum initial data has a zero‐dispersion limit characterized by Lax and Levermore as the solution of an infinite‐dimensional constrained quadratic minimization problem. An adaptive numerical method for computing the weak limit from this characterization is constructed and validated. The method is then used to study the weak limit. Initial simple experiments confirm theoretical predictions, while experiments with more complicated data display multiphase behavior considerably beyond the scope of current theoretical analyses. The method computes accurate weak limits with multiphase structures sufficiently complex to provide useful test cases for the calibration of numerical averaging algorithms. © 1994 John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)1319-1364
Number of pages46
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 1994

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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