@article{Al-Sawalha2024, 
author = {M. Mossa Al-Sawalha and Safyan Mukhtar and Albandari W. Alrowaily and Saleh Alshammari and Sherif. M. E. Ismaeel and S. A. El-Tantawy},
title = {Analytical solutions to time-space fractional Kuramoto-Sivashinsky Model using the integrated Bäcklund transformation and Riccati-Bernoulli sub-ODE method},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12357-12374},
keywords = {fractional Kuramoto-Sivashinsky (KS) equation, Bäcklund transformation, Riccati-Bernoulli sub-ODE method, shock and periodic waves, families of traveling wave solutions},
url = {https://www.sciopen.com/article/10.3934/math.2024604},
doi = {10.3934/math.2024604},
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.}
}