The tanh–coth and the sine–cosine methods for kinks, solitons, and periodic solutions for the Pochhammer–Chree equations

In this paper, the tanh–coth method and the sine–cosine method are used for a reliable treatment of the Pochhammer–Chree equations which include a variety of models. Travelling wave solutions of distinct structures, namely bell-shaped solitons, kink-shaped solitons, and periodic solutions are formally derived. The two methods demonstrate power, reliability and efficiency.