Extension of the sine-Gordon expansion scheme and parametric effect analysis for higher-dimensional nonlinear evolution equations

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics

“…Also researchers have developed several effective, powerful and efficient exact methods for uncovering the solutions of these equations. Notable techniques encompass the Jacobi elliptic function expansion scheme 30 , the Hirota bilinear method 31 , the exp-function method 32 , the new extended algebraic method 33 , the unified method 34 , the -expansion technique 35 , the auxiliary equation outline 36 , the Darboux transformation technique 37 , the Bäcklund transformation 38 , the modified extended tanh technique with Riccati equation 39 , the generalized -expansion approach 40 , the modified Kudryashov method 41 – 43 , the sine–Gordon expansion method 44 , the modified sine–cosine method 45 , the consistent Riccati expansion solvability technique 46 , the modified sine–Gordon expansion approach 47 , the modified simple equation method 48 – 50 , the generalized Kudryashov method 51 – 53 , among others.…”

The Extended Direct Algebraic Method for Extracting Analytical Solitons Solutions to the Cubic Nonlinear Schrödinger Equation Involving Beta Derivatives in Space and Time

“…The soliton solutions derived from FNLEE have practical and commercial applications in various fields such as optical fiber technology, telecommunications, signal processing, image processing, system identification, water purification, plasma physics, medical device sterilization, chemistry, and other related domains [1,2]. Various dynamic approaches have been introduced and implemented in the literature to solve nonlinear fractional differential equations (NFDES) and obtain analytical traveling wave solutions, for example, the exp-function method [3], the Modified Exp-function method [4], the inverse scattering transformation method [5,6], the Bäcklund transformation method [7], the homogenous balance method [8,9], the Jacobi elliptic function method [10], the unified algebraic method [11], the sine-cosine method [12,13], the tanh-coth method [14,15], improved modified extended tanh-function method [16,17], the Lie symmetry analysis method [18], the extended generalized (G /G)-expansion method [19], the modified simple equation method [20], the generalized Kudryashov method [21,22], the sine-Gordon expansion method [23], the Riccati-Bernoulli equation method [24,25], the new extended direct algebraic method [26,27], and the new auxiliary equation method [28].…”

Solitons of the Jimbo-Miwa Equation through the Sine-Gordon Expansion Scheme

“…Moreover, four different lump-type solutions to the (3+1)-dimensional JM equation were obtained using the Hirota bilinear form [7]. There are many methods [16][17][18][19][20] have been established to investigate the nonlinear evolution equations (NLEEs) by several mathematicians and physicists. To our knowledge, the (3+1)-dimensional JM equation has not yet been solved by using the sine-Gordon expansion scheme.…”