Spectral algorithm for two-dimensional fractional sine-Gordon and Klein–Gordon models

M. A. Abdelkawy, H. Almadi, E. M. Solouma and M. M. Babatin
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M. A. Abdelkawy: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia†Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
H. Almadi: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
E. M. Solouma: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia†Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
M. M. Babatin: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 12, 1-16

Abstract: Solitons and waves with memory effects are two examples of nonlinear wave phenomena that can be studied mathematically using the fractional nonlinear sine-Gordon equation. It is a modification of the traditional sine-Gordon equation that takes memory effects and nonlocal interactions into account by adding fractional derivatives. A more complex explanation of particle dynamics and interactions within relativistic quantum mechanics is made possible by the fractional Klein–Gordon model, a theoretical framework that expands the standard equation to include fractional derivatives. The study uses shifted Legendre–Gauss–Lobatto and shifted Legendre–Gauss–Radau collocation techniques to solve numerically two-dimensional sine-Gordon and Klein–Gordon models. The study handles two-dimensional sine-Gordon and Klein–Gordon models by extending a collocation approach using basis functions. It suggests a collocation technique that uses a suggested basis to automatically satisfy the conditions. The suggested methods’ spectral accuracy and efficiency are validated by numerical results.

Keywords: Two-dimensional fractional sine-Gordon and Klein–Gordon models; shifted Legendre and Legendre polynomials; Caputo fractional (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124501493

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