Preprint C11/2002
Propriedades das soluções de uma equação de Schrödinger não-linear de alta ordem

Xavier Carvajal

**Keywords: **
Nonlinear Schródinger equation

We study properties of solutions for a higher order nonlinear Schrodinger
equation. When the coefficients appearing in the linear terms of the equation
are smooth functions of time, we establish local well-posedness for the
associated initial value problem (IVP) with data in Sobolev spaces of order
greater or equal than one fourth. We also consider the equation with constant
coefficients and show that the local solutions of the IVP can be extended
globally in Sobolev spaces of index greater than five ninth. Other problem we
consider here is related to unique continuation principles. In particular, we
prove that solutions of the IVP with compact support in two different times
have to be zero. Finally, we investigate whether or not the results obtained
for the IVP are the best possible and ill-posedness issues for the problem.