Formula_15307

\[\begin{gathered}\frac{\partial f_{k}}{\partial t}+v_{k} \frac{\partial f_{k}}{\partial x}=\frac{1}{2} \sum_{i+j=k} x_{i j} f_{i} f_{j}-f_{k} \sum_{i=1}^{\infty} x_{i j} f_{i}, \\k=1,2,3, \ldots,\end{gathered}\]