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Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

Xavier Carvajal
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Abstract

We prove that, the initial value problem associated to u_{t} + i\alphau_{xx} + βu_{xxx} + iγ|u|^{2}u = 0, x,t \in R, is locally well-posed in Sobolev spaces H^{s} for s>-1/4.

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Xavier Carvajal. 2003-07-31. Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices. https://arxiv.org/abs/math/0307400

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