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

A version of the method of the simplest equation called 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.