## 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.

### MSC:

 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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### References:

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