Abstract: Based on Lighthill's equation, the n-th order (n > 2) inhomogeneous wave equations are established by means of the perturbation method. The third-order nonlinear parameter C/A is defined as a new characteristic parameter in addition to the second-order one B/A, By using the Lagrange's parameter variation method, the third-order harmonic waves are obtained, in which the accumulation solution have a term proportional to the square of the distance, It is shown by analysis that all the solutions are valid only in the region where the accumulation terms are predominant.