New solitonic and rogue wave solutions of a Klein–Gordon equation with quadratic nonlinearity

Abstract An analytical investigation is performed on soliton, lump wave solution, and rogue waves in the Klein-Gordon with quadratic nonlinearity through the extended tanh approach, which possesses complicated wave propagation arising in the field of nonlinear optics, theory of quantum field and solid state physics. As a result, an advanced form of interacting analytical solutions is achieved with some unrestricted parameters. Different conditions on the existing parameters of these solutions are found after analyzing its dynamic behavior. Based on the conditions, different type of rogue wave, bright bell and dark bell shape nature of the solutions are considered. The dynamics nonlinear wave solutions are showed in 3D plots with specific values of the existing parameters. Moreover, it is shown that nonlinear wave packets are localized in two dimensions with characteristics of rogue wave profiles.