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

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2021-06, Vol.3, p.100036, Article 100036
• Main Authors: Roshid, M.M., Karim, M.F., Azad, A.K., Rahman, M.M., Sultana, Tahmina
• Format: Article
• Language: English
• Subjects: Bright and dark bell shape; Klein–Gordon equation (KGE); Lump; Nonlinear wave; Rogue wave; The extended tanh method (E-tanh); Theory of quantum field
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2021.100036

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. •Extended tanh (E-tanh) method.•The new traveling wave solutions.•Traveling wave results through exponential function with some free parameters.•Different type rogue wave solution that might be vital to describe some•Sophisticated nonlinear physical phenomena.