This paper applies the generalized exp(−φ (ξ ))-expansion technique to urge accurate and numerical wave solutions for (3 + 1)-dimensional breaking soliton wave equation, Korteweg-de Vries equation and extended Korteweg-de Vries-Kadomtsev-Petviashvili equation with particle-like behaviour for constructing novel solitary wave solutions of these essential models. These equations describe the propagation of fragile dispersive and small amplitude waves in a very similar 3-dimensional medium that plays a significant role in mathematical physics. The generalized exp (−φ (ξ ))-expansion technique is compelling, fabulous, happy and efficient to encourage precise and travelling wave resolution of partial nonlinear differential equations (PDEs.). We tend to compare the results of this new technique and another technique and show that, however, the closure of this technique ends up hiding many alternative strategies in this field.