Math @ Duke

Publications [#244153] of Stephanos Venakides
Papers Published
 Tovbis, A; Venakides, S, The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases,
Physica D: Nonlinear Phenomena, vol. 146 no. 14
(2000),
pp. 150164 [doi]
(last updated on 2018/07/17)
Abstract: In this paper, we study the semiclassical limit of the ZakharovShabat eigenvalue problem for the focusing of NLS with some specific initial data. In all these cases, the eigenvalue problem is reduced to connection problems for the hypergeometric equation and for other classical equations. The special initial data [Suppl. Prog. Theor. Phys. 55 (1974) 284] is contained in our family of initial data, parameterized by a real parameter μ, as a particular case μ=0. We find that beyond a certain value of the parameter μ, the purepoint spectrum becomes empty and all the scattering information is contained in the reflection coefficient.


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