https://doi.org/10.1140/epjp/s13360-022-03285-3
Regular Article
Analytical and numerical-simulation studies on a combined mKdV–KdV system in the plasma and solid physics
1
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, Xuzhou, China
2
Department of Basic Science, Obour High Institute for Engineering and Technology, 11828, Cairo, Egypt
a
mostafa.khater2024@yahoo.com
Received:
29
June
2022
Accepted:
14
September
2022
Published online:
23
September
2022
Using the extended truncated expansion approach and three precise B-spline numerical methods, this paper examines the structure of the analytical and numerical solutions to the combined mKdV equation and KdV equation. This model represents the propagation of weakly nonlinear long waves in a KdV-typed medium by changing the coefficients of dispersion and nonlinear coefficients. Additionally, it also describes the flow below a pressure surface in a fluid. The numerical schemes of ExCBS, SBS, and TQBS are used. The handled model may describe many different phenomena, including the propagation of a thermal pulse through a single sodium fluoride crystal and the motion of confined particles under a harmonic force in a one-dimensional nonlinear lattice. The link between fast and slow soliton, which causes a phase shift, is shown in several instances. The energy density along the route of rapid and slow colliding solitons is shown to be very small and relatively large, respectively, thanks to the phase shift shown by the contour map. If the analytical and numerical solutions vary by the same amount, then the spline-connected and distribution graphs will be consistent.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
