Solitary wave solution of the KdV-BBM equation with triangular fuzzy number incorporation

Purpose The study aims to investigate the solitary wave solution of the Korteweg-de Vries–Benjamin-Bona-Mahony Equation (KdV-BBME) in the context of shallow water waves, incorporating both crisp and fuzzy parameters to analyse the wave characteristics. Design/methodology/approach The paper employs the homotopy perturbation transform method (HPTM) alongside its fuzzy counterpart (fuzzy homotopy perturbation transform method) for handling the stated problem. Findings A series-type solution of KdV-BBME is found using HPTM and FHPTM. Numerical results show the effectiveness of FHPTM in capturing uncertainties, with results comparable to both exact and existing numerical solutions, particularly when bench-marked against the Adomian Decomposition Method. Originality/value The fuzzy KdV-BBME is formulated by introducing uncertainties in places of key parameters like wave amplitude and Stokes–Ursell number coefficients. Involved uncertainties are addressed using a double parametric approach, highlighting how fuzziness affects the shape and behavior of the solitary wave.