A fuzzy semi-analytical approach for modeling uncertainties in solitary wave solution of coupled nonlinear Boussinesq equations

Abstract This article presents the precise solitary wave solution (SWS) of nonlinear coupled Boussinesq equations (BEs) in shallow water using the Homotopy Perturbation Transform Method (HPTM) and Fuzzy HPTM (FHPTM). The study introduces a fuzzy model for the coupled BEs by incorporating uncertainties in wave depth coefficients. The effectiveness of FHPTM is demonstrated through a comparison with the exact solution for the crisp case, using the double parametric approach to highlight the fuzziness in the solution. Numerical results under various scenarios are examined to understand the behavior of the SWS. HPTM results are compared with those derived from the Adomian Decomposition Method (ADM). The results show good agreement with both exact and numerical techniques.