Application of the modified method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg - de Vries equation and generalized Camassa-Holm equation

Abstract: The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh - equation are used as simplest equations. Some of the obtained solutions correspond to surface water waves.