Generalised exponential rational function method for obtaining numerous exact soliton solutions to a ( $$3+1$$ 3 + 1 )-dimensional Jimbo–Miwa equation

In this work, we apply the generalised exponential rational function (GERF) method on an extended ( $$3+1$$ )-dimensional Jimbo–Miwa (JM) equation which describes the modelling of water waves of long wavelength with weakly nonlinear restoring forces and frequency dispersion. This JM equation is also used to construct modelling waves in ferromagnetic media and two-dimensional matter-wave pulses in Bose–Einstein condensates. The main purpose is to construct analytical wave solutions for the ( $$3+1$$ )-dimensional JM equation by utilising the GERF method with the help of symbolic computations. We have also presented three-dimensional plots to observe the dynamics of obtained results. To understand physical phenomenon through different shapes of solitary waves, we discussed solitons, the interaction of multiwave solitons, lump-type solitons and kink-type solutions.