Singular solitons of Biswas-Arshed equation by the modified simple equation method

Construction of bright-dark solitary waves and elliptic function solutions of space-time fractional partial differential equations and their applications

“…Many efficient and powerful methods have been established and improved for finding their exact solutions such as simple equation method [24], modified simple equation method [25], extended simple equation method [26], direct algebraic method [27], extended mapping method [28], ¢ G G ( )-expansion method [29],…”

Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics

“…Physicists, engineers and mathematicians have established precise solutions for the NLEEs that transform into a key task in the analysis of nonlinear physical incidents. Generally, there is no single approach to resolve all sorts of NLEEs, and a variety of scientific groups have successfully established many techniques, including the method of extended tanh-function [1], the method of tanh function [2,3], the method of sine-cosine [4], the method of modified extended tanh function [5], the method of exp (−ϕ(ξ ))-expansion [6], the method of exp-function [7], the method of Backlund transformation [8], the method of Miura transformation [9], the method of extended F-expansion [10], the method of improved F-expansion [11], the method of ( ′/ / G G G , 1 )-expansion [18], the method of (G′/G)expansion [12][13][14][15], the method of new auxiliary equation [16], the method of auxiliary equation [17], the method of Kudryashov [18][19][20][21], the method of modified Kudryashov [29], the method of extended trial function [31], the method of variational iteration [32], the method of modified simple equation (MSE) [22][23][24][25][26][27][28][29][30][31][32], extended modified direct algebraic method, extended mapping method and Seadawy techniques to find solutions for some nonlinear partial differential equations [33][34]…”

Highly dispersive solitons in polarization-preserving fibers by Adomian decomposition method

“…The presented results depict the complete interpretation of bright solitons. The error plots show the precision of analytical results with the ADM. Additionally, distinguished numerical methods will be implemented to explore the analytical outcomes like the variational iteration method, finite element method, and finite difference method that are based on the reported results [16][17][18][19][27][28][29][30][31][32].…”