Multiple-soliton solutions of two extended model equations for shallow water waves

Multiple-soliton solutions for two extensions of model equations for shallow water waves, presented in [M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur, The inverse scattering transform – Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974) 249–315; R. Hirota, J. Satsuma, N-soliton solutions of model equations for shallow water waves, J. Phys. Soc. Jpn. 40 (2) (1976) 611–612] are obtained. The two extensions possess identical dispersion relations but with different structures for the N  -soliton solutions for N>1N>1. The Hirota bilinear method is used to determine multiple-soliton solutions of sech-squared type for these extended equations. The tanh–coth method is used to obtain single soliton solutions.