New revelations and extensional study on the recent sixth-order 3D Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation

This study makes consideration of the recently devised Lax-integrable three-dimensional sixth-order Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation owing to the great relevance of higher-dimensional nonlinear evolution equation models in guiding various nonlinear phenomena in scientific domains. Thus, as only a little is known about the new model, the present study is therefore, obliged to unravel more about the admissibility of supplementary exact solutions by the model through the use of the promising Kudryashov method. In fact, all the special models arising from the governing equation have been reduced with regard to both the equations as well as the corresponding exact solutions. In addition, the study graphically analyses the state of the art with regard to the temporal variation as well as the influence of the Kudryashov-index on the evolution of waves associated with the model. Lastly, the model of concern is further extended to the n-dimensional frame and equally analyzed using the adopted methodology.