Protracted study on a real physical phenomenon generated by media inhomogeneities

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.