Preprint A263/2003
On the Cauchy problem for a coupled system of KdV equations

Mahendra Panthee | Linares, Felipe

**Keywords: **
KdV equation | Cauchy problem

We study some questions related to the well-posedness for the initial value
problem associated to the system
\begin{equation}
\begin{cases}
u_{t}+u_{xxx}+a_3v_{xxx}+uu_{x}+a_1vv_{x}+a_2(uv)_x =0,\\
b_1v_{t}+v_{xxx}+b_2a_3u_{xxx}+vv_{x}+b_2a_2uu_{x}+b_2a_1(uv)_x=0.
\nonumber
\end{cases}
\end{equation}
Using recent methods, we prove a sharp local result in Sobolev
spaces. We also prove global result under some conditions on the
coefficients.