Abstract
We search for traveling-wave solutions of the class of PDEs ∑ p = 1 N 1 A p ( Q ) ∂ p Q ∂ t p + ∑ r = 2 N 2 B r ( Q ) ∂ Q ∂ t r + ∑ s = 1 N 3 C s ( Q ) ∂ s Q ∂ x s + ∑ u = 2 N 4 D u ( Q ) ∂ Q ∂ x u + F ( Q ) = 0 where A p ( Q ) , B r ( Q ) , C s ( Q ) , D u ( Q ) and 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.
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