7 citations · 7 across the 2 of their papers we have counts for
2 papers
math.AP2005
Sharp global well-posedness for a higher order Schrödinger equation
Xavier Carvajal
Using the theory of almost conserved energies and the ``I-method'' developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher…
math.AP2003★ 7 cited
Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices
Xavier Carvajal
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.