Abstract
We consider the initial value problem (IVP) associated with a higher order non-linear Schrödinger (h-NLS) equation∂tu+ia∂x2u+b∂x3u=2ia|u|2u+6b|u|2∂xu,x,t∈R, with given data in the modulation space Ms2,p(R). Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces Ms2,p(R) for s≥14 and p≥2.
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