Abstract
An approximate wave equation ux+(a/x) u − (β/c02)uut′ = 0, where t′ =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 coordinate x be 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.
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