W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

Abstract

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

Optical Solitons and Single Traveling Wave Solutions for the Fiber Bragg Gratings with Generalized Anticubic Nonlinearity

“…where C 0 is the integral constant. Plugging (18) and ( 19) into (17), we can get a polynomial about U, denoted by GðUÞ. Using the balance principle, we get m = 3.…”

“…3 Advances in Mathematical Physics Integrating formula (26), we obtain optical solitons and exact traveling wave solutions [12][13][14][15][16][17] of Equation (3) under nine cases. Details will be given in the next section.…”

A New Computational Technique for Analytic Treatment of Time‐Fractional Nonlinear Equations Arising in Magneto‐Acoustic Waves

“…Te phenomenon of nonlinear equations describes the fundamental physical aspects in nature ranging from chaotic behaviour in biological systems [15], plasma physics-plasma containment in stellarators, and tokamaks to energy generation [16,17], quantum mechanics [18], nonlinear optics [19], solid-state physics and up to fbre optical communication devices [20], dual wave soliton solution [21], unidirectional shallow water waves [22], analytical wave solutions [23], unmagnetized dust plasma [24], optimal solitons for the nonlinear dynamics [25], and so on [26][27][28]. Te various phenomena of nonlinear equations are modelled in terms of many orders of nonlinear partial diferential equations ( 29)- (31).…”

The modified extended tanh technique ruled to exploration of soliton solutions and fractional effects to the time fractional couple Drinfel'd–Sokolov–Wilson equation

“…The NLEEs equation has not yet been solved using such a technique. Due to this, several researchers have created a variety of trustworthy, effective, and simple methods for solving NLEEs equations like as the procedure of enhanced (G ′/G)-expansion [ 13 ], the manner of modified Kudryashov [ 14 ], the procedure of modified simple equation [ 15 ], the procedure of sine-Gordon equation expansion [ 16 ], the procedure of extended sinh-Gordon equation expansion [ 17 ], the manner of exp -expansion [ 18 ], the new auxiliary equation and modified Kudryashov scheme [ 19 ], MSE scheme [ 20 ], the trial solution formula [ 21 ], the procedure of Frobenius integrable decomposition [ 22 ], – expansion and Sine-Gordon-expansion methods [ 23 ], the manner of multiple simplest equation [ 24 ], the manner of solitary wave ansatzes [ 25 ], the manner of simple equation [ 26 ], the manner of extended simplest equation [ 27 ], the scheme of modified extended tanh-function [ 28 ], the manner of Hirota [ [29] , [30] , [31] , [32] ], new extended direct algebraic method [ 33 ], MSE method [ 34 ], the tanh-coth method [ 35 ], Riemann-Hilbert problems [ [36] , [37] , [38] , [39] ] and so on. As a result, nonlinear science is emerging as one of the fundamental areas of research in the growing wave system.…”