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Computing the weak limit of KdV
Author(s) -
McLaughlin David W.,
Strain John A.
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160471003
Subject(s) - limit (mathematics) , mathematics , korteweg–de vries equation , quadratic equation , simple (philosophy) , estimator , characterization (materials science) , mathematical optimization , mathematical analysis , nonlinear system , geometry , physics , philosophy , statistics , epistemology , quantum mechanics , optics
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.