Local and global well posedness results are established for the initial-value problem associated to the 1D Zakharov-Rubenchik system. We show that our results are sharp in some situations by proving ill-posedness results otherwise. The global results allow us to study the norm growth of solutions corresponding to the Schrödinger equation term. We use ideas recently introduced to study the classical Zakharov systems.
"Well posedness for the 1D Zakharov-Rubenchik system." Adv. Differential Equations 14 (3/4) 261 - 288, MArch/April 2009. https://doi.org/10.57262/ade/1355867267