Math @ Duke

Publications [#244294] of Xin Zhou
Papers Published
 Tovbis, A; Venakides, S; Zhou, X, On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation,
Communications on Pure and Applied Mathematics, vol. 57 no. 7
(2004),
pp. 877985, ISSN 00103640 [doi]
(last updated on 2018/08/18)
Abstract: We calculate the leadingorder term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit for a certain oneparameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t ≥ 0. We utilize the RiemannHilbert problem formulation of the inverse scattering problem to obtain the leadingorder term of the solution. Error estimates are provided. © 2004 Wiley Periodicals, Inc.


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