Two new reductions methods for polynomial differential equations and applications to nonlinear PDEs

The new methods have been applied to obtain some reductions and, consequently, new solutions for three polynomial ordinary differential equations related to well-known equations in mathematical physics: the Kuramoto-Sivashinsky equation, a generalized Benney equation and a 5th-order KdV equation. Some pieces of computer algebra code, written in Maple and implementing the underlying algorithms to derive the reductions, are also included.