Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method

• Published in: Results in physics Vol. 25; p. 104228
• Main Authors: Ali Akbar, M., Akinyemi, Lanre, Yao, Shao-Wen, Jhangeer, Adil, Rezazadeh, Hadi, Khater, Mostafa M.A., Ahmad, Hijaz, Inc, Mustafa
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-06-2021; Elsevier
• Subjects: Soliton solutions; The Boussinesq equation; The GK method; The SGE method; The SGE method; Soliton solutions; The GK method; The Boussinesq equation
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104228

•The Boussinesq equation is studied.•The bell-shape soliton, kink, singular kink, compacton, contracted bell-shape soliton, periodic soliton, anti-bell shape soliton, and other shape solitons are retrieved.•The sine-Gordon expansion and the generalized Kudryashov methods are presented.•The obtained solutions are presented by 2D and 3D figures.
The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. In this article, the sine-Gordon expansion (SGE) approach and the generalized Kudryashov (GK) scheme are used to establishbroad-spectral solutions including unknown parameters and typical analytical solutions are recovered as a special case. The well-known bell-shape soliton, kink, singular kink, compacton, contracted bell-shape soliton, periodic soliton, anti-bell shape soliton, and other shape solitons are retrieved for the definite value of these constraints. The 3D and contour plots of some of the results obtained are sketched by assigning individual values of the parameter and analyzed the dynamical behavior of the waves. Furthermore, the compatibility of the two approaches has been compared and examined the efficiency to ascertain soliton solutions.