Publications [#139800] of Stephanos Venakides

Papers Published

1. A. Tovbis, S. Venakides, X. Zhou, On the long time limit of semiclassical (zero dispersion limit) solutions of the focusing Nonlinear Schroedinger Equation: Pure radiation case., vol. 59 no. 10 (2006), pp. 1379 - 1432 [MR2248894]
   (last updated on 2007/12/17)

   Abstract:
   In a previous paper [13] we calculated the leading-order term q0(x,t,) of the solution of q(x,t,), the focusing nonlinear (cubic) Schrödinger (NLS) equation in the semiclassical limit ( 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,) 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.