An approximate wave equationux+(a/x) u − (β/c02)uut′ = 0, wheret′ =t − x/c0, is derived for progressive plane (a= 0), spherical (a= 1), and cylindrical(a = 12)waves of finite amplitude in a lossless fluid. In the case of spherical and cylindrical waves, it is required that the spatial coordinatexbe large. Solutions of the equation satisfying an arbitrary but given boundary condition are obtained. When the source excitation is sinusoidal, generalized Bessel‐Fubini solutions may be found. Another set of exact solutions is found that corresponds to a sawtooth wave. From these solutions, amplitude‐decay formulas are derived that agree with results obtained previously by Mendousse, Rudnick, Westervelt, and Naugol'nykli.