Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson–Pickering equation

• Published in: Results in physics Vol. 44; p. 106193
• Main Author: Khater, Mostafa M.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2023; Elsevier
• Subjects: Approximate solution; Camassa–Holm equation; Fornberg–Whitham equation; Rosenau–Hyman equation; Soliton wave; Soliton wave; Camassa–Holm equation; Fornberg–Whitham equation; 35Q51; Approximate solution; 35Q60; 35C08; Rosenau–Hyman equation; 35E05
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2022.106193

In this study, we use cutting-edge analytical and numerical approaches to the Gilson–Pickering (GP) problem in order to get precise soliton solutions. This model explains wave propagation in plasma physics and crystal lattice theory. A variety of evolution equations have been developed from the GP model, including the Fornberg–Whitham (FW) equation, the Rosenau–Hyman (RH) equation, and the Fuchssteiner-Fokas-Camassa–Holm (FFCH) equation, to name a few. The GP model has been studied using these evolution equations. To investigate the characterizations of new waves, crystal lattice theory and plasma physics use the Khater II, and He’s variational iteration approaches. Many alternative responses may be achieved by utilizing various formulae; each of these solutions is shown by a distinct graph. The validity of such methods and solutions may be demonstrated by assessing how well the relevant techniques and solutions match up. The results of this study suggest that the technique is preferred for successfully resolving nonlinear equations that emerge in mathematical physics. •Study of the nonlinear Gilson–Pickering equation.•Analytical and numerical novel constructed results.•Investigating the obtained results’ accuracy.•Explaining the obtained solutions through some distinct types of sketches.•Crystalline solid vibrates as a wave passes through its atoms in plasma.