**Papers Published**

- Tovbis, A; Venakides, S; Zhou, X,
*On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case*, Communications on Pure and Applied Mathematics, vol. 59 no. 10 (October, 2006), pp. 1379-1432, WILEY, ISSN 0010-3640

(last updated on 2019/06/16)**Abstract:**

In a previous paper [13] we calculated the leading-order 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 one-parameter 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 long-term behavior of the semiclassical solution q(x, t, ε) in the pure radiation case. As before, our main tool is the Riemann-Hilbert 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.