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Semiclassical Limit of the Focusing Nonlinear Schrödinger Equation under Barrier Initial Data
We study the semiclassical behavior of the focusing nonlinear Schrödinger equation in 1+1 dimensions under discontinuous "barrier" initial data and we describe the violent oscillations arising in terms of theta functions. The construction of proofs relies on the analysis of the associated Riemann-Hilbert factorization problem.