Dynamics and control of interaction waves in sixth-order nonlinear Ramani equation

In this work, an integrable sixth-order nonlinear Ramani equation is investigated by constructing the interaction solutions through Hirota’s bilinear form along with a generalized test function consisting of polynomials, trigonometric and hyperbolic functions. The obtained solutions admit several arbitrary free parameters, which can be utilized to control the nature of associated nonlinear waves. A categorical analysis revealed the possibility of getting various physically interesting nonlinear wave profiles such as bright, dark, kink-type solitary waves and their interactions for suitable choices of parameters are explored in detail with appropriate graphical demonstrations.