Abstract
This article examines the approximate solution of the Geophysical Korteweg-de Vries (GKdV) equation in a fuzzy environment. The Adomian decomposition method (ADM) and ADM-Pade approximation technique have been implemented to solve the governing equation. Environmental or climate changes, along with the propagation of air or water waves, can lead to uncertainties or ambiguities in initial or boundary conditions, as well as in parameter associated with the Coriolis effect. To address these uncertainties, this work aims to find the approximate fuzzy solution to the said physical problem by applying a double parametric approach with the help of ADM. To validate the obtained solution, comparisons are made between the fuzzy solutions and existing precise (crisp) solutions in specific cases. Furthermore, in another scenario involving the fuzzy solution, the ADM-Pade approach is employed. This implementation yields an approximate solution that exhibits higher accuracy and closely resembles a solitary wave solution, demonstrating a rapid convergence rate. The analysis of special cases shows a direct relationship between wave height and the Coriolis parameter and an inverse relationship between wavelength and the Coriolis parameter. Finally, the article includes 2D and 3D graphs, along with plots of fuzzy solutions, to enhance understanding of the fuzzy nature of the solutions.
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The first author extends thanks to the University Grants Commission (UGC), New Delhi, India, for supporting their daily expenses throughout the research period.
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Sahoo, M., Chakraverty, S. Influence of uncertain coriolis parameter on wave solution of Korteweg-de Vries equation. Int J Geomath 15, 10 (2024). https://doi.org/10.1007/s13137-024-00252-1
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DOI: https://doi.org/10.1007/s13137-024-00252-1
Keywords
- Geophysical Korteweg-de Vries equation
- Uncertain Coriolis parameter
- Fuzzy set
- Triangular Fuzzy number
- Adomian decomposition method
- Pade- approximation