Infinitesimal weak symmetries, of nonlinear differential equations in two independent variables

Non-classical infinitesimal weak symmetries of PDE introduced by Olver and Rosenau (1987) are analysed. In the case of PDE in two independent variables, it is demonstrated that obtaining such symmetries is equivalent to obtaining the two-dimensional modules of non-classical partial symmetries. The Boussinesq and the nonlinear heat equations are treated from the point of view of non-classical symmetries.