Formula_18053

\[\begin{gathered}m \frac{\partial^{2} f_{0}}{\partial \tau^{2}}+\mathscr{F}_{u}^{\prime}\left(f_{0}, x\right)=0, \quad m=S_{t}^{2}-(\nabla S)^{2}, \\L f_{k} \stackrel{\operatorname{def}}{\equiv} m \frac{\partial^{2} f_{k}}{\partial \tau^{2}}+\mathscr{F}_{u u}^{\prime \prime}\left(f_{0}, x\right) f_{k}=R_{k} .\end{gathered}\]