In this paper, we study the solution of nonlinear equation k u(x)=f(x,Δ k - 1 k u(x)) where k is the Diamond operator iterated k times and is defined by k = i = 1 p 2 x i 2 2 - j = p + 1 p + q 2 x j 2 2 k or the operator k can be expressed by k = k Δ k =Δ k k . The operators Δ k and k are Laplacian and the ultrahyperbolic operator iterated k times, defined by k = 2 x 1 2 + 2 x 2 2 +...+ 2 x p 2 - 2 x p + 1 2 - 2 x p + 2 2 -...- 2 x p + q 2 k and Δ k =( 2 x 1 2 + 2 x 2 2 +...+ 2 x n 2 ) k ,p+q=n is the dimension of the n-dimensional Euclidean space R n ,x=(x 1 ,x 2 ,...,x n ) R n ,k is a nonnegative integer, u(x) is an unknown and f is a given function. It is found that, the existence of the solution u(x) of such equation depending on the conditions of f and Δ k - 1 k u(x) and moreover such solution u(x) related to the wave equation depending on the conditions of p,q and k.