Symmetries and soliton solutions of nonlinear equations

A new, purely algebraic method is developed for finding soliton solutions of nonlinear equations; it does not require the use of the formalism of the inverse scattering method. As examples, explicit expressions for soliton solutions are constructed for some wellknown equations as well as some not hitherto discussed in the literature. The symmetry basis of the method is associated with infinite-dimensional Lie algebras, these being internal symmetry algebras of the systems considered.