Analytical and Numerical Solution to the Generalized Logarithmic Regularized Boussinesq Equation with Coefficients Estimation

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DOI: https://doi.org/10.28924/2291-8639-24-2026-154
Published: May 20, 2026
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Sharefa Asiri, M. S. Ismail, H. A. Ashi, Analytical and Numerical Solution to the Generalized Logarithmic Regularized Boussinesq Equation with Coefficients Estimation, Int. J. Anal. Appl., 24 (2026), 154.

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Sharefa Asiri, M. S. Ismail, H. A. Ashi

Abstract

The logarithmic regularized Boussinesq equation (Log-RBE) is a partial differential equation that is used to describe the propagation of long ocean waves, like tsunamis, in coastal regions. In this paper, we first generalize the Log-RBE by considering model coefficients. Then, an exact Gaussian solitary wave solution is derived. Additionally, the implicit Crank-Nicolson finite difference (CNFD) scheme is employed to obtain a numerical solution that approximates the exact one. Furthermore, we study the identifiability of the model’s coefficients, which leads to two estimation problems. Then, the modulating function method (MFM) is applied to address these estimation problems. All the theoretical findings were complemented by numerical experiments. The CNFD scheme’s efficiency goes beyond its accuracy to the ease of its implementation and the short CPU time consumed to find the approximate solution. In addition, the MFM solutions to the coefficient estimation problems show satisfactory results even in the presence of noisy measurements.

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