Abstract
In the work that we are doing now, our goal is to find a solution to the (3 + 1)-dimensional Sakovich equation, which is an equation that can be used to characterize the movement of nonlinear waves. This approach sees extensive use across the board in engineering's many subfields. This new equation can represent more dispersion and nonlinear effects, which allows it to accept more different application scenarios. As a result, it has a wider range of potential applications in the physical world. As a consequence of this, when the two components are combined, they can be used to easily counteract the effects of nonlinearity and dispersion on the integrability of partially differential equations. This equation represents a novel physical paradigm that should be looked into further. We use the following three analytical techniques: the exp-?? expansion method is the first one, the second is the G '/kG '+G+r expansion method, and the Bernoulli sub-ODE technique is the last one. Lastly, the soliton solutions obtained are presented by graphs in two and three dimensions, which present different kinds of solitons such as dark, periodic, exponential, bright, and singular soliton solutions.