On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation

Abstract

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.