Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation Original Research Article

The matrix Riemann-Hilbert factorization approach is used to derive the leading-order, exponentially small asymptotics as t → ± ∞ such that x/t ∼ O(1) of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation, i∂tu + ∂x2u − 2(|u|2 − 1)u = 0, with finite density initial data u(x,0) = x→±∞exp(i(1 ∓ 1)φ/2)(1+o(1)), φϵ [0, 2π).