Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach

Abstract

In this work, we investigate the dynamical study of the (1+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation via the unified method is investigated. This technique is used to obtain the soliton solutions, including the trigonometric function solution, the periodic function solution, the exponential function solution, the elliptic function solution, and other soliton-form solutions. All the obtained results in this work utilizing an effective unified method help gain a better understanding of the physical meaning and behavior of the equation, thus sheding light on the significance of investigating diverse nonlinear wave phenomena in physics and ocean engineering. These derived results are entirely new and never repeated in the previous works done by the other authors. For the interest of visual presentation and physical illustrations, we plot the graphical demonstrations of some of the specified solutions in 3-dimensional, contour, and 2-dimensional plots by using Mathematica software. Consequently, we observe that the acquired solutions of the MNW equations are anti-bell-shape, kink wave solution, solitary wave, periodic solution, multisoliton, and different types of soliton solutions.

Optical soliton solutions of fokas system and (2 + 1) Davey-Stewartson system by mapping method

“…Optical solitons have showed significant effect in telecommunication field because of its key role in data transmission through optical fibers over large distances, such passing through oceans and from one continent to other without loss of data [1][2][3][4]. Many researchers working hard to derive variety of new solutions of these models such as Hussain et al [5] solved nonlinear pseudo-parabolic partial differential equations by using extended direct algebraic method, Gasmi et al [6] studied nonlinear (1+1)-dimensional Phi-four equation in the sense of Katugampola operator, Kumar et al [7] studied ( ) + 1 1 dimensional Mikhailov-Novikov-Wang equation to generate soliton solutions, Sivasundaram et al [8] studied complex properties to the first equation of the Kadomtsev-Petviashvilli hierarchy. Therefore, to find optical solitons and other exact solutions of NLPDEs, many powerful analytical methods have been developed such as Ansatz method [9], tanh expansion method [10], tan(f/2)-expansion method [11], variational iteration method [12], exp(−Φ(ξ)) method [13], Jacobi elliptic function method [14], (G′G)-expansion method [15], Modified Kudryashov method [16], sine-Gordon expansion method [17], Auxiliary equation method [18], improved tanh(j(ξ)/2)-expansion method [19].…”

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

“…For deeper consideration of nonlinear occurrence and realistic challenges, it is essential to discover closed-form soliton solutions of SFPDEs. According to the quick advancements in nonlinear sciences, a variety of simple and efficient approaches have been developed to obtain closed-form soliton solutions to NLPDEs, including the Hirota method [4,5], the Bernoulli sub-equation method [6,7], the F-expansion method [8], the (G ′ /G 2 )-expansion method [9], the simple equation method [10], the modified auxiliary equation method [11,12], the two variable (G ′ /G, 1/G)-expansion method [13][14][15][16], the Lie symmetric analysis [17], the polynomial complete discriminant system [18], the tanh-coth scheme [19], the Conservation laws method [20], the generalized exponential rational function approach [21,22], the binary bell polynomials method [23], the mapping method [24], the Shehu transform scheme [25], the sine-Gordon expansion [26], the Cole-Hopf transformation method [27,28], the Fan subequation technique [29], the unified method [30], the Khater method [31], the r + mEDAM method [32], the spectral Tau method [33], the G ′ G ′ +G+A -expansion procedure [34][35][36][37][38], the sub-equation method [39], the collocation method [40], the finite element method [41], and the generalized G ′ /G-expansion method …”