Abstract
In this work, the ( 3 + 1 )-dimensional Wazwaz–Benjamin–Bona–Mahony equation is formulated in the sense of conformable derivative. Two novel methods of generalized Kudryashov and exp − φ ℵ are investigated to obtain various exact soliton solutions. All algebraic computations are done with the help of the Maple software. Graphical representations are provided in 3D and 2D profiles to show the behavior and dynamics of all obtained solutions at various parameters’ values and conformable orders using Wolfram Mathematica.
Highlights
Partial differential equations (PDEqs) have attracted a particular interest from researchers in the fields of natural sciences and engineering due to the applicability of these equations in modeling various scientific phenomena in interdisciplinary sciences such as mathematical physics, mechanics, signal and image processing, and chemistry
Most physical systems are not linear; nonlinear partial differential equations (NLPDEqs), nonlinear evolution equations (NLEEqs), have inspired researchers to investigate the existence of exact solutions for such equations
Finding new exact solutions for NLPDEqs can significantly provide a good interpretation for the physical meaning and dynamics of these equations
Summary
Partial differential equations (PDEqs) have attracted a particular interest from researchers in the fields of natural sciences and engineering due to the applicability of these equations in modeling various scientific phenomena in interdisciplinary sciences such as mathematical physics, mechanics, signal and image processing, and chemistry. To solve nonlinear integrable equations, a novel technique, known as Hirota bilinear method, was proposed by Ma and Ma et al in [5, 6] in order to obtain new lump solutions for the investigated equations [7]. Equation (1) was first proposed by Wazwaz [10] by formulating a new three-dimensional modified version of BBMEqs, known as the Wazwaz-Benjamin-Bona-Mahony equation (WBBMEq), via coupling or various generalized contexts or as combination of both of them. Inspired by all above studies, this work is mainly aimed at obtaining new exact solitary solutions for a version of WBBMEq formulated in the sense of conformable derivative (ComD) with the help of two novel techniques: generalized Kudryashov method and expð−φðאÞÞ method.
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