The tanh and sine-cosine methods for higher order equations of Korteweg-de Vries type

The aim of this paper is twofold. Firstly, the tanh method with the aid of Mathematica is used to obtain exact soliton solutions for a new fifth-order nonlinear integrable evolution equation. Secondly, the sine-cosine and the rational sine-cosine methods are proposed for constructing more general exact solutions of the soliton type for two nonlinear evolution equations arising in nonlinear science and theoretical physics, namely the symmetric regularized long wave equation and a new model of the Korteweg-de Vries type, which gives a more realistic version of shallow water waves.