Abstract
In this work, we study the dynamical behavior for a real physical application due to the inhomogeneities of media via analytical and numerical approaches. This phenomenon is described by the 3D Date–Jimbo–Kashiwara–Miwa (3D-DJKM) equation. For analytical techniques, three different methods are performed to get hyperbolic, trigonometric and rational functions solutions. After that, the obtained solutions are graphically depicted through 2D- and 3D-plots and numerically compared via the finite difference algorithm to check the precision of the proposed methods.
•Different wave structures for abundant solutions to the (3+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation are investigated.•Performance was done by using the strategy of three different analytical methods.•Numerical solutions were introduced via the finite difference method.•Physical explanations are discussed for the obtained solutions.