Decouple Three Partial Differential Equations

Question

How to decouple this system so I can get three decoupled equations of the following forms: $q_1$= function of $q_1$, $q_2$= function of $q_2$ and $p$= function of $p$. \begin{eqnarray} &&q_{1t}=(q_{1,xx}+3pq_{1})_x,\\ &&q_{2t}=(q_{2,xx}+3pq_{2})_x,\\ &&p_t=(p_{xx}+\frac{3}{2}p^2+a_1q_1^2+a_2q_2^2)_x \end{eqnarray} Any ideas to separate these equations in terms of $q_1, q_2$, and $p$? Thanks a lot.