New wave solutions, exact and numerical approximations to the nonlinear Klein-Gordon equation - Partohaghighi, Mohammad; Sulaiman, Tukur A.; Yusuf, Abdullahi; İnç, Mustafa; Bayram, Mustafa (World Scientific Publ Co Pte Ltd, 2023)
This study investigates the nonlinear Klein-Gordon equation (KGE). We successfully construct some new topological kink-type, non-topological, singular solitons, periodic waves and singular periodic wave solutions to this nonlinear model by using the extended ShGEEM, rational sine-cosine extended (ERSC), and sinh-cosh (ERSCh) methods. In addition, a numerical method for solving the KGE is described in this paper. We use a combination of two numerical techniques called fictitious time integration method and the group preserving scheme (GPS). Fictitious time integration method converts the main equation into a new problem then the GPS is used to gain the numerical solutions. Few experiments are provided to successfully demonstrate the correctness of the approach.
Keywords: ShGEEM; extended rational sine-cosine; sinh-cosh; KGE; Group preserving scheme; Fictitious time integration method (FTIM)