On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation: Pure radiation case
Abbreviated Journal Title
Commun. Pure Appl. Math.
ASYMPTOTICS; Mathematics, Applied; Mathematics
In a previous paper  we calculated the leading-order term q(0)(x, t, epsilon) of the solution of q (x, t, epsilon), the focusing nonlinear (cubic) Schrodinger (NLS) equation in the semiclassical limit (epsilon -> 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, epsilon) 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." (c) 2006 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
"On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation: Pure radiation case" (2006). Faculty Bibliography 2000s. 6654.