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English

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

Analysis of PDEs 2007-05-23 v1

Authors: Xavier Carvajal

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Abstract

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

Keywords

nonlinear schrodinger equation well-posedness sobolev spaces initial value problem negative indices

Cite

@article{arxiv.math/0307400,
  title  = {Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices},
  author = {Xavier Carvajal},
  journal= {arXiv preprint arXiv:math/0307400},
  year   = {2007}
}