The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line

Abstract

We prove local well-posedness for the initial-boundary-value problem associated to some quadratic nonlinear Schrödinger equations on the half-line. The results are obtained in the low regularity setting by introducing an analytic family of boundary forcing operators, following the ideas developed by Colliander, Kenig and Holmer.

28 pages, revised version, referee suggestions, will appear in Differential and Integral Equations

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