Novel analytical approximations to the nonplanar Kawahara equation and its plasma applications
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
2 Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
3 King Abdullah City for Atomic and Renewable Energy (K.A.CARE), Riyadh, Saudi Arabia
4 Department of Physics, Faculty of Science, Port Said University, 42521, Port Said, Egypt
5 Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, 1988, Al-Baha, Saudi Arabia
Accepted: 2 October 2022
Published online: 23 October 2022
In this paper, some novel analytical approximations to a completely non-integrable nonplanar (cylindrical and spherical) Kawahara equation (nKE) are derived. Using the ansatz method, a new hypothesis is introduced in order to obtain high-accurate approximations. Based on the proposed method, two analytical approximations are obtained. All obtained approximations can recover all traveling wave solutions to the nKE. For evaluating the accuracy of the obtained approximations, the residual error is determined. Moreover, the analytical approximations are compared to the finite difference scheme approximation. Numerous researchers can benefit from the obtained results to understand the scenario of propagating several nonlinear phenomena such as the cylindrical and spherical cnoidal waves, solitons, etc. in fluids mechanics and plasma physics.
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