Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space. (English) Zbl 1038.35113

The authors obtain long-time asymptotics for solutions \(q(x,t)\) of the defocusing nonlinear Schrödinger equation for initial data with sufficient smoothness and decay as \(t\) approaches to infinity. They describe a new technique which produces an error estimate of order \(O(t^{-((1/2)-k)})\) for any \(0<k<1/4\), under the assumption that the initial data \(q_0\) lies in a weighted Sobolev space.


35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35Q15 Riemann-Hilbert problems in context of PDEs
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