Abstract
The current study deals with investigation of Einstein's vacuum field equation (EVFE) for exploring various lumps, breathers and interaction solutions via bilinear method and choosing appropriate polynomial function. In particular, we obtain lump, lump 1-strip, lump 2-strip, lump periodic, Manifold periodic, rogue wave (RW), generalized breather, Akhmediev breather, Ma breather, Kuznetsov-Ma breather and its corresponding RW solutions for ensuing model. In addition, we also made interaction among lump, periodic and kink-wave with their numeric simulation. In general relativity, the governing model play momentous part in many ambitious experiments and space missions. Furthermore, distinct other random parameters give enough choice to manipulate physical states governed by this model are observed.