  Kinetic Vlasov equation for collisional Maxwellian plasmas is used. Collision
integral of BGK (Bhatnagar, Gross and Krook) type is applied. From Vlasov
equation we find distribution function of electrons in square-law approximation
on size of transversal electric field. The formula for electric current
calculation is deduced. This formula contains an one-dimensional quadrature. It
is shown, that nonlinearity leads to revealing of the longitudinal electric
current directed along a wave vector. This longitudinal current is
perpendicular to known so-called transversal classical current. The classical
current turns out at the linear analysis. The longitudinal current in case of
small values of wave numbers is calculated. When frequency of collisions tends
to zero, all received formulas for collisional plasmas pass in the known
corresponding results for collisionless plasmas. Graphic research of
dimensionless density of a current is carried out.
