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The behavior of the weyl function in the zero-dispersion KdV limit
- Source :
- Comm. Math. Phys. 183, no. 1 (1997), 119-143
- Publication Year :
- 1997
- Publisher :
- Springer Science and Business Media LLC, 1997.
-
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.
- Subjects :
- Dirichlet problem
34A55
Logarithm
Mathematical analysis
Zero (complex analysis)
Statistical and Nonlinear Physics
Function (mathematics)
Measure (mathematics)
35B25
34L25
Moment (mathematics)
35Q53
Nonlinear Sciences::Exactly Solvable and Integrable Systems
35P20
Limit (mathematics)
Korteweg–de Vries equation
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 14320916 and 00103616
- Volume :
- 183
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....95ab88e44355abb23e9b1e1d2ff775f3