Math @ Duke

Publications [#244290] of Xin Zhou
Papers Published
 with Tovbis, A; Venakides, S; Zhou, X, On the longtime limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case,
Communications on Pure & Applied Mathematics, vol. 59 no. 10
(2006),
pp. 13791432, ISSN 00103640 [doi]
(last updated on 2017/12/17)
Abstract: In a previous paper [13] we calculated the leadingorder term q 0(x, t, ε) of the solution of q(x, t, ε), the focusing nonlinear (cubic) Schrödinger (NLS) equation in the semiclassical limit (ε → 0) 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. The aim of the present paper is to calculate the longterm behavior of the semiclassical solution q(x, t, ε) in the pure radiation case. As before, our main tool is the RiemannHilbert problem (RHP) formulation of the inverse scattering problem and the corresponding system of "moment and integral conditions," known also as a system of "modulation equations." © 2006 Wiley Periodicals, Inc.


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