We consider the plasma heating nonlinearities that are important in ma
ny wave-interaction processes. By means of some simple examples, we an
alyse the nonlinear terms originating from the collision integral for
a weakly collisional plasma. As a result, it turns out to be necessary
to generalize the collisional Zakharov equations by including the con
tribution from the non-diagonal part of the pressure tensor. A new sys
tem of equations is thus presented.