Abstract
•We present application in mathematical physics models.•Higher order first and second order PDE equations.•Solitary wave solutions.•The hydrodynamic mathematical methods.•Modulation instability analysis.
In this study, we implement the generalized (G′/G)-expansion method established by Wang et al. to examine wave solutions to some nonlinear evolution equations. The method, known as the double (G′/G, 1/G)-expansion method is used to establish abundant new and further general exact wave solutions to the (3 + 1)-dimensional Jimbo–Miwa equation, the (3 + 1)-dimensional Kadomtsev–Petviashvili equation and symmetric regularized long wave equation. The solutions are extracted in terms of hyperbolic function, trigonometric function and rational function. The solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite values. Graphs of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic, anti-kink, singular soliton, singular anti-bell shape, compaction etc. This method is straightforward, compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.