The behavior of the Weyl function in the zero-dispersion KdV limit

Nicholas M Ercolani, C. David Levermore, Taiyan Zhang

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The moment formulas that globally characterize the zero-dispersion limit of the Korteweg-deVries (KdV) equation are known to be expressed in terms of the solution of a maximization problem. Here we establish a direct relation between this maximizer and the zero-dispersion limit of the logarithm of the Jost functions associated with the inverse spectral transform. All the KdV conserved densities are encoded in the spatial derivative of these functions, known as Weyl functions. We show the Weyl functions are densities of measures that converge in the weak sense to a limiting measure. This limiting measure encodes all of the weak limits of the KdV conserved densities. Moreover, we establish the weak limit of spectral measures associated with the Dirichlet problem.

Original languageEnglish (US)
Pages (from-to)119-143
Number of pages25
JournalCommunications in Mathematical Physics
Volume183
Issue number1
StatePublished - 1997

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Weyl Function
Weak Limit
Zero
Limiting
Korteweg-Devries equation
Spectral Measure
Dirichlet problem
Logarithm
Dirichlet Problem
logarithms
Transform
Moment
Converge
Derivative
moments

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

The behavior of the Weyl function in the zero-dispersion KdV limit. / Ercolani, Nicholas M; Levermore, C. David; Zhang, Taiyan.

In: Communications in Mathematical Physics, Vol. 183, No. 1, 1997, p. 119-143.

Research output: Contribution to journalArticle

Ercolani, Nicholas M ; Levermore, C. David ; Zhang, Taiyan. / The behavior of the Weyl function in the zero-dispersion KdV limit. In: Communications in Mathematical Physics. 1997 ; Vol. 183, No. 1. pp. 119-143.
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