Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics

• Published in: Results in physics 2021-01, Vol.20, p.103762, Article 103762
• Main Authors: Kayum, Md. Abdul, Ara, Shamim, Osman, M.S., Akbar, M. Ali, Gepreel, Khaled A.
• Format: Article
• Language: English
• Subjects: Gas dynamics equation; Klein–Gordon equation; Nonlinear evolution equations; Sine-Gordon expansion method; Solitons
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2020.103762

•The broad-ranging general stable soliton solutions to some nonlinear equations have been established associated with parameters and integral constants in physics and gas dynamics.•The characteristics of gas flow ensuing shock fronts and nonlinear optics have been analysed.•The 3D and contour plots of the obtained solutions are depicted to illustrate profile of the phenomena. Stable soliton solutions for the nonlinear Klein–Gordon equation in condensed matter physics, particle physics, nonlinear optics, solid state physics and the gas dynamics equation ensuing in shock fronts have been established by putting use of the sine-Gordon expansion procedure. We establish the broad-ranging familiar stable wave solutions related with some free parameters, for particular values of which some of the subsisting solutions in the literature are re-established and several fresh solutions are formulated. The contour and 3D shapes are depicted to describe the physical phenomena of the established solutions. Scores of solitary wave solutions are obtained such as, compacton, smooth soliton, anti-bell type solitary wave, bell-type solitary wave, kink and some other new types of solitary wave solutions. The obtained results might play important role in optics, quantum mechanics, mathematical physics and engineering. It is noticeable to inspect that the sine-Gordon expansion procedure is an efficient, competent and straightforward mathematical tool to ascertain exact solitary wave solutions.