Preprint C18/2003
On Some Nonlinear Dispersive Systems
Adán José Corcho
Keywords: well-posedness | Ill-Posedness Solitary Waves | Schrodinger-KdV | Schrodinger-Debye
We study local and global well-posedness of the initial value problem (IVP) associated to the coupled Schrodinger-Korteweg-de Vries equation and Schrodinger-Debye systems. We also consider the Benney system and discuss some ill-posedness issues regarding this system. For the coupled Schrodinger-Korteweg-de Vries equation we obtain a local result for weak initial data that allows to use the conserved quantities in the energy space to prove global well-posedness in that space. Both results considerably improve the previous ones, obtained by Bekiranov and Tsutsumi. Concerning the Schrodinger-Debye systems we also obtain local and global results improving the ones given by Bidegaray. The techniques used to prove our results are recents argument introduced by Bourgain, Kenig, Ponce and Vega to study general nonlinear dispersive equations.