Math @ Duke

Publications [#10184] of Stephen P. Shipman
Papers Published
 Stephen P. Shipman, The Spectral Transform in the Semiclassical Limit of a Finite Discrete NLS Chain,
Physica D: Nonlinear Phenomena, Vol. 162, Nos 12 (2002), 95129
[physd]
(last updated on 2002/07/06)
Abstract: The linear spectral problem associated with the inverse
solution of a finite discrete nonlinear Schroedinger chain
is studied in the semiclassical limit. The discrete
spectral problem is a recursion relation for a vector
quantitiy, with boundary conditions, depending on intial
data and a spectral parameter. WKB analysis is performed
and then interpreted for the case that the quantities in the
chain are less than one in modulus. In this case, the
spectrum lies on the unit circle and an aymptotic density is
obtained. The density is supported by known facts about the
discrete spectra, numerical results, and regorous results
concerning the asymptotics of the solution of the spectral
boundaryvalue problem. In addition,the norming constants
in the spectral transform are positive in this special case,
and a proposed asymptotic norming exponent is corroborated
by numerical data.


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