the generalized (2 + 1) and (3+1)-dimensional with advanced analytical wave solutions via computational applications

The analytical solutions for an important generalized nonlinear evolution equations nlees dynamical partial differential equations (dpdes) that involve independent variables represented by the (2 + 1)-dimensional breaking soliton equation, the (2 + 1)-dimensional calogero--bogoyavlenskii--schiff  (cbs) equation, and the (2 +1)-dimensional bogoyavlenskii’s breaking soliton equation (be), and some new exact propagating solutions to a generalized (3+1)-dimensional kp equation with variable coefficients are constructed by using a new algorithm of the first integral method (nafim) and determined some analytical solutions by appointing special values of the parameters. in addition to that, we showed a new variety and unique travelling wave solutions by graphical illustration with symbolic computations.