Publications [#244294] of Xin Zhou

Papers Published

1. 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 (July, 2004), pp. 877-985, WILEY, ISSN 0010-3640
   (last updated on 2024/04/18)

   Abstract:
   We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit 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. We utilize the Riemann-Hilbert problem formulation of the inverse scattering problem to obtain the leading-order term of the solution. Error estimates are provided. © 2004 Wiley Periodicals, Inc.