Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

“…In order to make sense of the obtained solutions physically by using MSSEM, we presented them in the figures 5-10. Consequently, the solutions obtained were in the form of optical dark solution for equation (34) and equation (45) as presented in figures 1 50), (51) and equation (55). In figure 5, the effect for different values of t are presented for equation (42), we concluded that when the time increased the wave solution is also increased.…”

“…The Sardar sub-equation method is a powerful technique to obtain exact solutions of nonlinear PDEs [40][41][42][43][44][45][46][47][48][49][50][51][52]. A new modification of this method was proposed in a recent study, which involves using a new trial solution ansatz that includes arbitrary functions.…”

“…expansion method [11,12], the Bernoulli subequation function method [13], the generalized exponential rational function method [14-16], the ¢ -( ) G 1 expansion method [17, 18], Hirota's simple method [19][20][21], and other methods [22][23][24][25][26][27] have been used to obtain solutions for these NPDEs. Additionally, the Jacobi elliptic function expansion method (JEFEM) has been applied to several NPDEs, including the Biswas-Arshed equation in [28], various nonlinear wave equations such as KdV, mKdV equations, Boussinesq model and nonlinear klein-gordon equation [29], the fourth-order NPDE and the Kaup-Newell equation in [30], and other related studies [31][32][33][34][35][36][37][38].Similarly, the new modification of the Sardar sub-equation method (MSSEM) has also been applied to several NPDEs such as the generalized unstable nonlinear Schrodinger equation in [39], the perturbed Fokas-Lenells equation in [40], the Korteweg-de Vries equation in [41], the Benjamin-Bona-Mahony equation and the Klein-Gordon equations in [42], the Klein-Fock-Gordon equation in [43], the Boussinesq equation in [44], the perturbed Gerdjikov-Ivanov equation in [45], and other related studies [46][47][48][49][50][51][52].…”

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

“…Using symbolic tools, several suitable and efficient techniques for finding the appropriate solutions to various NLEEs have been demonstrated. There are several effective techniques, such as the Hirota bilinear technique (HBT) 8 , 9 , the modified Sardar sub-equation technique 10 , 11 , the hyperbolic-function technique 12 , the amended -Gordon expansion technique 13 , 14 , the Jacobi’s elliptic expansion technique 15 , 16 , the modified Fan-sub expansions technique 17 , 18 , the modified Kudryashov technique 19 , the Khater method 20 , the modified simple equation technique 21 , the unified Riccati equation expansion technique 22 and so on 23 , 24 . The authors in 25 studied the dynamical structure of soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+ 1)-dimensional Konopelchenko-Dubrovsky (KD) model.…”

Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion

“…Furthermore, analytical and numerical schemes enlarging incessantly in the literature have crucial in examining soliton solutions of diverse NLSEs. Researchers have evolved diverse analytical and numerical approaches to acquire different soliton forms Such as, the new Kudryashovʼs scheme [10], the enhanced Kudryashovʼs approach [11,12], the improved extended Tanh-function technique [13], the extended trial function scheme [14], the unified Riccati equation expansion aprroach [15][16][17][18][19], the auxiliary equation technique [20], the Melnikov method [21], the generalized Kudryashov technique [22], the Kudryashov method [23], the enhanced modified extended tanh expansion approach [24][25][26][27], the Sardar sub-equation scheme [28][29][30][31], the Painlevé test approach [32][33][34][35].…”