Multiple-soliton solutions for the fifth order Caudrey–Dodd–Gibbon (CDG) equation

In this work we use the Hirota’s direct method combined with the simplified Hereman method to determine the N-soliton solutions for the fifth order Caudrey–Dodd–Gibbon (CDG) equation. The one-soliton solution will be handled by the tanh–coth method. The work highlights the significant features of the employed methods.