Solitary waves of the complex Ginzburg-Landau equation with anti-cubic nonlinearity

On optical soliton solutions of the higher-order Lakshmanan-Porsezian-Daniel model having the cubic-quintic-septic law in the presence of spatio-temporal and chromatic dispersion

“…These equations help researchers and engineers understand the conditions under which solitons can form and propagate. Schrödinger-Hirota [1,2], the complex Ginzburg-Landau [3], Radhakrishnan-Kundu-Lakshmanan [4], Biswas-Arshed [5,6], Biswas-Milovic [7], Kadomtsev-Petviashvili equation with variable coefficients [8], Sasa Satsuma [9][10][11], Chen-Lee-Liu [12,13], the Kundu-Mukherjee-Naskar [14], the Fokas-Lenells [15][16][17] the modified Korteweg-de Vries [18] and Lakshmanan-Porsezian-Daniel [19] equations are some of the important models.…”

Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis

“…For this, investigators have succeeded in finding solutions for the NLEEs using a variety of analytical and numerical methods. Among many techniques, there are some efficient and powerful schemes which are the improved modified extended tanh-function [ 1 ], the new extended generalized Kudryashov [ 2 ], the unified [ 3 ], the enhanced Kudryashovs [ 4 ], the linear superposition principle and weight algorithm [ 5 ], the AAE [ 6 ], the modified extended auxiliary equation mapping [ 7 ], the Sardar sub-equation [ 8 ], the GERF and modified auxiliary equation [ 9 ], the improve F -expansion [ 10 ], the Hirota’s bilinear [ 11 ], the modification of the simplest equation [ 12 ], the Darboux transformation [ 13 ] and numerous other approaches. Among the many techniques, our stated techniques are effective and powerful to obtain exact/soliton solutions from the NLEEs.…”