with the initial conditions

  and 

where    is the n-dimensional Euclidean space,  is the Diamond operator iterated k-times defined by

 can be written as the product of the operators in the form    where  is the Laplacian and  is the ultra-hyperbolic.  c is a positive constant, k is a nonnegative integer, f and g are continuous and absolutely integrable functions. We obtain  as a solution for such equation. Moreover, by e-approximation we also obtain the asymptotic solution    In particularly, if we put    and  then the  reduces to the solution of the biharmonic wave equation