一个非线性色散波方程的惟一连续性

该文证明:和如下耦合色散系统相联系的初值问题的充分光滑的解$(u,v)=(u(x,t),v(x,t))$, 如果在两个时刻有半线支集那么它们全为零. {? _tu+?³_x u+? _x(u^p v^p+1)=0, ? _tv+?³_x v+?_x(u^p+1v^p)=0,x∈R,t≥ 0

On the Unique Continuation Property for a Nonlinear Dispersive System

It is proved that, if a sufficiently smooth solution $(u,v)=(u(x,t),v(x,t))$ to the initial value problem associated with the dispersive coupled system {? _t u+?³_x u+? _x(u^p v^p+1)=0,  ? _t v+?³_x v+?_x(u^p+1v^p)=0,        x ∈R, t ≥ 0 is supported on a half line at two different instants of time then u ≡ 0, v ≡ 0.