The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis

Abstract

The Estevez-Mansfield-Clarkson (EMC) equation and the (2+1)-dimensional Riemann wave (RW) equation are important mathematical models in nonlinear science, engineering and mathematical physics which have remarkable applications in the field of plasma physics, fluid dynamics, optics, image processing etc. Generally, through the sine-Gordon expansion (SGE) method only the lower-dimensional nonlinear evolution equations (NLEEs) are examined. However, the method has not yet been extended of finding solutions to the higher-dimensional NLEEs. In this article, the SGE method has been developed to rummage the higher-dimensional NLEEs and established steady soliton solutions to the earlier stated NLEEs by putting in use the extended higher-dimensional sine-Gordon expansion method. Scores of soliton solutions are figure out which confirms the compatibility of the extended SGE method. The solutions are analyzed for both lower and higher-dimensional nonlinear evolution equations through sketching graphs for alternative values of the associated parameters. From the figures it is notable to perceive that the characteristic of the solutions depend upon the choice of the parameters. This study might play an impactful role in analyzing higher-dimensional NLEEs through the extended SGE approach.

Examination of Kraenkel-Manna-Merle System by Sine-Gordon Expansion Method

“…Si and Li constructed the one-soliton and two-soliton for KMM system by the bilinear method [28]. In this study, we will use SGEM, which is one of the widely used methods to find the solutions of NLEEs [29][30][31][32]. SGEM has been grown based on traveling wave transformation and the sine-Gordon equation [33].…”

Abundant optical soliton solutions to the fractional perturbed Chen-Lee-Liu equation with conformable derivative

“…The acquisition of soliton solutions for important equations is now a highly researched field among academics. A number of scholars have provided justification for a variety of sophisticated methods to investigate soliton solutions, including the Hirota's process [1], the sine-Gordon expansion technique [2,3], the first-integral approach [4,5], the auxiliary equation technique [6,7], the sine-cosine scheme [8,9], and the generalized Kudryashov procedure [10,11], the ( ) ¢ G G -expansion approch [12,13], the extended tanh-function scheme [14,15], the f 6 -model expansion method [16], the Jacobielliptic function expansion technique [17,18], the exponent function process [19], the ( ) ¢ G G G , 1 -expansion method [20,21], the generalized ( ) ¢ G G -expansion technique [22], the modified extended tanh-function method [23,24], and many others.…”

Abundant explicit solutions for the M-fractional coupled nonlinear Schrödinger–KdV equations

“…The Bäcklund transformation method, 18 Darboux transformation, 19 and Hirota bilinear method 20 can be used to find the N-soliton solutions. The improved F-expansion method, 21 projective Riccati equations method, 22 Jacobi elliptic function expansion method, 23 Gʹ/G-expansion method, 24 (d + Gʹ/G)-expansion method, 25 (Gʹ/G, 1/G)-expansion method, 26 sine Gordon method, 27 Lie symmetry method, 28 new Kudryashov's method, 29 auxiliary equation method, 30 exponential rational function method, 31 etc. [32][33][34][35][36][37][38][39][40][41][42] can be used to find doubly periodic solutions, solitary wave solutions, and trigonometric function solutions of these models.…”