Analytic study of the fifth order integrable nonlinear evolution equations by using the tanh method

Abstract

The tanh method is used to derive explicit travelling wave solutions for two fifth order integrable nonlinear evolution equations. The fifth order KdV equation (fKdV) and the fifth order Caudrey–Dodd–Gibbon (CDG) equation are used as vehicles for our analysis. New families of solitary wave solutions and periodic solutions are formally obtained for these equations. The presented framework reveals quite a number of useful features of the method used here.