The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves

Multiple-soliton solutions for three model equations for shallow water waves are determined. The three models are completely integrable. The Hirota bilinear method is used to determine multiple-soliton solutions of sech-squared type for these equations. The tanh–coth method is used to obtain single soliton solutions and other solutions for these three models. The three models have different linear dispersion relations, but possess the same coefficients for the polynomials of exponentials.