Formula_807

\[\begin{gathered}\frac{\partial N}{\partial t}+v(\theta) \nabla_{x} N=\frac{c S}{\pi} \int_{0}^{2 \pi} N(x, \varphi, t) N(x, \varphi+\pi, t) d \varphi- \\-2 c S N(x, \theta, t) N(x, \theta+\pi, t) .\end{gathered}\]