The Cole–Hopf transformation and multiple soliton solutions for the integrable sixth-order Drinfeld–Sokolov–Satsuma–Hirota equation

The completely integrable sixth-order nonlinear Drinfeld–Sokolov–Satsuma–Hirota equation is studied. Three distinct methods, namely the Cole–Hopf transformation method, the tanh–coth method, and the Exp-function method are used for a reliable treatment of this equation. Solitons, multiple soliton solutions, multiple singular soliton solutions, and plane periodic solutions are obtained for this equations. The study highlights the power of each method.