On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations

We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases