Analytical solutions to time-space fractional Kuramoto-Sivashinsky Model using the integrated Bäcklund transformation and Riccati-Bernoulli sub-ODE method

M. Mossa Al-Sawalha; Safyan Mukhtar; Albandari W. Alrowaily; Saleh Alshammari; Sherif. M. E. Ismaeel; S. A. El-Tantawy; M. Mossa Al-Sawalha; Safyan Mukhtar; Albandari W. Alrowaily; Saleh Alshammari; Sherif. M. E. Ismaeel; S. A. El-Tantawy

doi:10.3934/math.2024604

AIMS Mathematics

2024, Volume 9, Issue 5: 12357-12374. doi: 10.3934/math.2024604

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Research article

Analytical solutions to time-space fractional Kuramoto-Sivashinsky Model using the integrated Bäcklund transformation and Riccati-Bernoulli sub-ODE method

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
4.
Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
5.
Department of Physics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
6.
Department of Physics, Faculty of Science, Ain Shams University, Cairo, Egypt
7.
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
8.
Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Baha 1988, Saudi Arabia

Received: 26 January 2024 Revised: 14 March 2024 Accepted: 18 March 2024 Published: 29 March 2024

This paper solves an example of a time-space fractional Kuramoto-Sivashinsky (KS) equation using the integrated Bäcklund transformation and the Riccati-Bernoulli sub-ODE method. A specific version of the KS equation with power nonlinearity of a given degree is examined. Using symbolic computation, we find new analytical solutions to the current problem for modeling many nonlinear phenomena that are described by this equation, like how the flame front moves back and forth, how fluids move down a vertical wall, or how chemical reactions happen in a uniform medium while they oscillate uniformly across space. In the field of mathematical physics, the Riccati-Bernoulli sub-ODE approach is shown to be a valuable tool for producing a variety of single solutions.
Citation: M. Mossa Al-Sawalha, Safyan Mukhtar, Albandari W. Alrowaily, Saleh Alshammari, Sherif. M. E. Ismaeel, S. A. El-Tantawy. Analytical solutions to time-space fractional Kuramoto-Sivashinsky Model using the integrated Bäcklund transformation and Riccati-Bernoulli sub-ODE method[J]. AIMS Mathematics, 2024, 9(5): 12357-12374. doi: 10.3934/math.2024604

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Abstract

This paper solves an example of a time-space fractional Kuramoto-Sivashinsky (KS) equation using the integrated Bäcklund transformation and the Riccati-Bernoulli sub-ODE method. A specific version of the KS equation with power nonlinearity of a given degree is examined. Using symbolic computation, we find new analytical solutions to the current problem for modeling many nonlinear phenomena that are described by this equation, like how the flame front moves back and forth, how fluids move down a vertical wall, or how chemical reactions happen in a uniform medium while they oscillate uniformly across space. In the field of mathematical physics, the Riccati-Bernoulli sub-ODE approach is shown to be a valuable tool for producing a variety of single solutions.

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