[en] A new extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation is obtained without any reference to the recursion operator or to the Lax operator formalism. Our method is based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogeneity dimensions. The non-polynomial densities with logarithmic behaviour are presented as an example. Special attention is paid to the singular case (γ = 1) for which we have found new non-homogeneous solutions expressed in terms of the elementary functions