Solitary wave structures in coupled burgers' equations with fuzzy parameters

Purpose The main purpose of this study is to develop an effective fuzzy-based technique for solving coupled Burgers' equations (cBEs) with uncertain parameters arising from measurement and observation errors, as well as environmental variability. Design/methodology/approach To solve the cBEs, uncertainty in the Stokes velocity due to gravity and Brownian diffusivity may result in variations in wave amplitudes and wave splitting, and such uncertainties cannot be neglected. To account for these uncertainties, the corresponding parameters are modeled as triangular fuzzy numbers (TFN) within a fuzzy framework. A fuzzy homotopy perturbation transform method (FHPTM) was used to obtain fuzzy series solutions to the cBEs. Findings The results showed that there was good convergence of the obtained solutions and that the convergent solutions determined through the FHPTM closely corresponded with exact and numerical solutions. Furthermore, the results demonstrate the impact of fuzziness in different parameters on wave behavior. The wave solution remains consistent and accurate for varying conditions. Originality/value This study presents that the a novel application of the FHPTM for solving fuzzy cBEs with uncertain parameters. The fuzzy technique produces lower and upper fuzzy bound solutions and offers novel insights into the effect of parameter uncertainty on wave propagation and stability of wave patterns.