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.
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Tovbis et al. (2004) studied this question.
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