N-soliton solutions for shallow water waves equations in (1 + 1) and (2 + 1) dimensions

A variety of shallow water waves equations in (1 + 1) and (2 + 1) dimensions are investigated. We first show that these models are completely integrable. We next determine multiple-soliton solutions for each equation. The simplified Hirota’s bilinear method developed by Hereman will be employed to achieve this goal. A comparison between dispersion relations and the phase shifts will be conducted. (But possess the same coefficients for the polynomials of exponentials.)