Hirota bilinear (HB) equation in its (3+1)-dimensional form is considered and analyzed. Travelling wave transformation has been employed to reduce the equation into an ordinary differential equation (ODE). Three distinct methods, the transformed rational function, Exp(−ϕ(ξ)) and (G′/G) expansion methods have been utilized to obtain analytical solutions. The solutions contain different types of wave solutions, N-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated.