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Publications [#10184] of Stephen P. Shipman

Papers Published

  1. Stephen P. Shipman, The Spectral Transform in the Semiclassical Limit of a Finite Discrete NLS Chain, Physica D: Nonlinear Phenomena, Vol. 162, Nos 1-2 (2002), 95-129 [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 boundary-value 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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