New exact solutions of the classical sine-Gordon equation in 2 + 1 and 3 + 1 dimensions

The method of Baecklund transformations is employed to derive in 2 + 1 and 3 + 1 dimensions exact solutions of the sine-Gordon equation (del/sup 2/ - c/sup -2/(partial/sup 2//partialt/sup 2/))chi = sinchi. A formula is developed in 3 + 1 dimensions which permits us to generate without additional quadratures an infinite class of new time-dependent solutions.