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<p>This study develops new semi-analytical and interval solutions for the coupled Drinfeld–Sokolov–Wilson Equations (DSWEs), which describe surface gravity waves moving horizontally on the seafloor. Seabed profiles vary across the sea, affecting wave propagation by altering wave amplitude and shape. Seabed profile may not be uniform across the sea. These variations in seabed profile may impact wave propagation such as change in wave amplitude and shape. So, considering initial condition as crisp based on particular seabed profile may lead to uncertain results. To handle this uncertainty, we considered coefficients in the initial condition as interval numbers. Elzaki Adomian Decomposition Method (EADM) and the Differential Quadrature Method (DQM) with Shifted Legendre Polynomials (SLP) at grid points are applied to solve the crisp and interval DSWEs. The results are compared with those from the Sumudu Adomian Decomposition Method (SADM), homotopy perturbation transform method (HPTM) and the exact solution. This study also analyzes the convergence of EADM solutions and the wave behavior of the wave amplitudes at each point.</p>

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Solution of coupled drinfeld–sokolov–wilson equations with imprecise parameters using semi analytical and numerical approaches

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Rambabu Vana,
  • Perumandla Karunakar

摘要

This study develops new semi-analytical and interval solutions for the coupled Drinfeld–Sokolov–Wilson Equations (DSWEs), which describe surface gravity waves moving horizontally on the seafloor. Seabed profiles vary across the sea, affecting wave propagation by altering wave amplitude and shape. Seabed profile may not be uniform across the sea. These variations in seabed profile may impact wave propagation such as change in wave amplitude and shape. So, considering initial condition as crisp based on particular seabed profile may lead to uncertain results. To handle this uncertainty, we considered coefficients in the initial condition as interval numbers. Elzaki Adomian Decomposition Method (EADM) and the Differential Quadrature Method (DQM) with Shifted Legendre Polynomials (SLP) at grid points are applied to solve the crisp and interval DSWEs. The results are compared with those from the Sumudu Adomian Decomposition Method (SADM), homotopy perturbation transform method (HPTM) and the exact solution. This study also analyzes the convergence of EADM solutions and the wave behavior of the wave amplitudes at each point.