c=2;l=30;
modell={u'[z]==v[z], v'[z]== - c v[z] - u[z] (1 - u[z]),
u[0]==0.999, v[0]==-0.001};
loesung=NDSolve[modell,{u,v},{z,0,l}]; 
abb=Plot[Evaluate[u[z]/.loesung],{z,0,l},
PlotPoints->50,PlotRange->All,
ImageSize->{400,300},AxesLabel->{"z","u"}];