On the unique continuation property for a nonlinear dispersive system

Abstract

We solve the following problem: If $(u,\,v)=(u(x,\,t),\,v(x,\,t))$ is a solution of the Dispersive Coupled System with $t_{1}<t_{2}$ which are sufficiently smooth and such that: $\operatorname{supp}u(\,.\,,\,t_{j})\subset (a,\,b)\,$ and $\,\operatorname{supp}v(\,.\,,\, t_{j})\subset (a,\,b),\,-\,\infty<a<b<\infty ,\,$ $j=1,\,2.\,$ Then $u\equiv 0$ and $v\equiv 0.$