The behavior of the weyl function in the zero-dispersion KdV limit |
| |
Authors: | Nicholas M Ercolani C David Levermore Taiyan Zhang |
| |
Institution: | (1) Department of Mathematics, University of Arizona, 85721 Tucson, AZ, USA;(2) Present address: Department of Mathematics, University of New Orleans, 70148 New Orleans, LA, USA |
| |
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.
Dedicated to Peter Lax on his 70th birthday |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|