Exact solutions of the Liouville equation in multidimensional spaces

Exact solutions of the multidimensional Lieu ville equation, which are soug ht in the class of functional forms of the degree n equal to the coordinate space dimension, are constructed based on a special representation of the Laplace and D'Alembert equations. The corresponding Liouville equation solu tions are completely described in the coordinate space dimensions d = 3,4. For d > 4, the general solution form and the method for obtaining algebraic equations for the coefficients of functional n-forms is presented.