Let's take into consideration the classical Boltzmann Equation for gas kinetics (i'm writing down the one obtained in Huang K. - Statistical mechanics, equation (3.36)):
$$\left(\frac{\partial}{\partial t} +\frac{\mathbf p_1}{m}\nabla_r+\mathbf F\nabla_{p_1} \right)f_1=\int d^3p_2 d^3p'_1 d^3p'_2 \delta^4(P_f-P_i)|T_{fi}|^2(f'_2f'_1-f_1f_2)$$
which is an integro-differential nonlinear (due to the $f'_2f'_1$ and $f_1f_2$ terms) equation in the distribution function $f_1$.
In a textbook I'm reading it is said that another feature of such equation is that
the nonlinear terms $f'_2f'_1$ and $f_1f_2$ are calculated for different values of the momentum.
What could be the meaning of this statement? Could "the momentum" be the $\mathbf p_1$ in $f_1(\mathbf x_1, \mathbf p_1, t$)?