Abstract

We study the smoothness properties of solutions to the coupled system of equations of Korteweg-de Vries type. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u0, v0 possesses certain regularity and sufficient decay as x ? 8, then the solution (u(t). v(t)) will be smoother than (u0, v0) for 0 < t = T where T is the existence time of the solution. © 2009 Royal Netherlands Academy of Arts and Sciences.