Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1)-dimensional WBBM equation

Abstract

The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the [Formula: see text]-fractional (3+1)-dimensional Wazwaz–Benjamin–Bona–Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using [Formula: see text], modified [Formula: see text] and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary wave, periodic wave, kink and antikink waves and most important supernonlinear periodic wave.

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

“…These solitons have revolutionized the telecom industry, leading to advancements in high-speed communication systems [16][17][18][19][20][21]. As a result, fractional-order NLPDEs have garnered attention in recent studies, particularly in optics and other applied sciences, owing to their potential applications in modeling highly nonlinear phenomena [22][23][24]. Fractional-order derivatives offer advantages over integer derivatives, providing more accurate mathematical and physical models for various technical issues [25][26][27].…”

Complex solutions for nonlinear fractional partial differential equations via the fractional conformable residual power series technique and modified auxiliary equation method

“…Analytical methodologies, new mathematical theories, and computational systems that enable us to study nonlinear complicated phenomena have triggered this revolution in understanding. Furthermore, the sub-equation Frontiers in Physics frontiersin.org method [19], modified Kudryashov method [20], and F-expansion method [21][22][23] are just a few of the methods that have been used. A semi-approximate approach called numerical simulations was developed specifically for addressing challenging nonlinear temporal FPDEs that can appear in a variety of scientific fields.…”