Smoothing properties for a coupled system of nonlinear evolution dispersive equations

摘要

We study the smoothness properties of solutions to the coupled system of equations of Kortewcg-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 (UIl, vol possesses certain regularity and sufficient decay as x -+ 00, then the solution (I<(f). v(t) will be smoother than (un, Vol for 0 < t ,,;;; T where T is the existence time of the solution.