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On the Construction of a Modulating Multiphase Wavetrain for a Perturbed Kdv Equation

  • David W. McLaughlin
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 2)

Abstract

This paper summarizes the status of a direct construction of an asymptotic representation of a modulating multiphase wavetrain for a class of perturbed kdV equations. This class includes the kdV-Burgers equation. The calculations apply on a “boundary” between dispersive and dissipative behavior. The construction proceeds by standard asymptotic methods. The result of the construction is an invariant representation of the reduced equations which permits their diagonalization. While mathematically the construction is incomplete, care is taken to identify the mathematical status of each step in the construction. The equivalence of this constructive approach with postulated averages of conservation laws is established for two phase waves. Finally, the Young measure for this program is constructed explicitly.

Keywords

Weak Limit Modulation Equation Phase Wave Young Measure Periodic Travel Wave Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • David W. McLaughlin
    • 1
  1. 1.Department of Mathematics and Program in Applied MathematicsUniversity of ArizonaTucsonUSA

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