Modified method of simplest equation and its application to nonlinear PDEs

We search for traveling-wave solutions of the class of PDEs∑p=1N1Ap(Q)∂pQ∂tp+∑r=2N2Br(Q)∂Q∂tr+∑s=1N3Cs(Q)∂sQ∂xs+∑u=2N4Du(Q)∂Q∂xu+F(Q)=0where Ap(Q),Br(Q),Cs(Q),Du(Q)Ap(Q),Br(Q),Cs(Q),Du(Q) and F(Q)F(Q) are polynomials of Q. The basis of the investigation is a modification of the method of simplest equation. The equations of Bernoulli, Riccati and the extended tanh-function equation are used as simplest equations. The obtained general results are illustrated by obtaining exact solutions of versions of the generalized Kuramoto–Sivashinsky equation, reaction–diffusion equation with density-dependent diffusion, and the reaction-telegraph equation.