Crighton (personal communication) has used a multiple‐time scales expansion to solve the problem of a plane periodic finite‐amplitude wave. We have adapted this method, applying a multiple‐length scales expansion to the three‐dimensional nonlinear wave equation derived by Westervelt [J. Acoust. Soc. Amer.25, 535 (1963)]. When the secular terms in the second‐order equation are set equal to zero, a simplified nonlinear equation is obtained. For the plane‐wave case, this equation leads to a solution essentially like that of Earnshaw [Trans. Roy. Soc. (London)150, 133–148 (1860)]. The method is used to obtain an “Earnshaw‐like” solution of the problems in which the linear farfield solution is a spherical wave whose amplitude contains a directivity factorD(θ). In particular, the method works for the farfield radiation from a piston, and the “Fubini‐like” solution for this problem is presented. Other applications are the radiating disk, the dipole, and arrays. The method is also applicable when the farfield wave is cylindrical. [This work was sponsored by the U. S. Air Force Office of Scientific Research.]