$ \left\{{ll} \partial_{t}u-\triangle_{x}u+b(t,x)\nabla_{x}u+V(x)u=G_{v} (t,x,u,v), \\ -\partial_{t}v-\triangle_{x}v-b(t,x)\nabla_{x}v+V(x)v=G_{u} (t,x,u,v), \right. {\forall}(t,x)\in\mathbb{R}
\times\mathbb{R}^{N}, $ \left\{\begin{array}{ll} \partial_{t}u-\triangle_{x}u+b(t,x)\nabla_{x}u+V(x)u=G_{v} (t,x,u,v), \\ -\partial_{t}v-\triangle_{x}v-b(t,x)\nabla_{x}v+V(x)v=G_{u} (t,x,u,v), \end{array}\right. {\forall}(t,x)\in\mathbb{R}
\times\mathbb{R}^{N}, |