Dynamical analysis of soliton structures for the nonlinear third-order Klein–Fock–Gordon equation under explicit approach

In this research, we utilized the auxiliary equation technique to invent the soliton results of the nonlinear third-order Klein–Fock-Gordon (KFG) equation. With the capability of explicit approach soliton results has been secured on the base of computational software. As a result, various solitary wave solutions are produced and shown in hyperbolic functions. The procedure delivers more general and wide-ranging soliton solutions separated with parameters and, for different values of constant parameters, reveals different shapes of solitons form, like dark soliton, bright soliton, combined bright and dark solitons and other types of solitons. It has been established that the method used to examine the nonlinear model is reliable, companionable, and reasonably good. Also, the method shows that it can be utilized on other types of nonlinear equations in a thorough way.