In this paper we discuss new applications of the nonclassical method of symmetry reduction. The equations treated are well known in mathematical physics and are used to describe multisoliton solutions of the Burger equation. They are also useful in the study of Kac-Moody algebras, and in the examination of nonlinear waves in the theory of elasticity. With the help of the nonclassical symmetry method the partial differential equations are reduced to ordinary differential equations which are solvable explicitly.