Open AccessThe zero dispersion limit for the Korteweg-deVries KdV equation
Author(s) -
Peter D. Lax,
C. David Levermore
Publication year - 1979
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.76.8.3602
Subject(s) - korteweg–de vries equation , limit (mathematics) , zero (linguistics) , dispersion (optics) , mathematics , mathematical analysis , inverse scattering problem , function (biology) , mathematical physics , inverse scattering transform , physics , inverse problem , quantum mechanics , linguistics , philosophy , nonlinear system , evolutionary biology , biology
We use the inverse scattering method to determine the weak limit of solutions of the Korteweg-deVries equation as dispersion tends to zero. The limit, valid for all time, is characterized in terms of a quadratic programming problem which can be solved with the aid of function theoretic methods. For larget , the solutions satisfy Whitham's averaged equations at some times and the equations found by Flaschkaet al. at other times.