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The concept of approximate symmetry is introduced. We describe all nonlinearities F (u) with which the non-linear wave equation 2u + λu 3 + εF (u) = 0 with a small parameter ε is approximately scale and conformally invariant. Some approximate solutions of wave equations in question are obtained using the approximate symmetry.

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Multiparametrical exact solutions of the many-dimensional nonlinear d'Alembert, Liouville, sine-Gordon and eikonal equations arc obtained. The maximally extensive local invariance groups of the equations are determined and invariants of the extended Poincaré group are found.

We present a compact and simple formulation of zero-and first-order conserved currents for the electromagnetic field and give the number of independent n-order currents.

The second-order partial differential equations invariant under transformations of Galilei, rotation, scale and projection are described.

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