Dispersive optical soliton solutions of the higher-order nonlinear Schrödinger dynamical equation via two different methods and its applications

M-shaped rational solitons and their interaction with kink waves in the Fokas–Lenells equation

“…By putting equations (11) and (5) into (2), we obtained the rational solution of equation (1) where the restricted conditions to avoid poles are b…”

“…Soliton solutions and their interactions are a central focus of nonlinear sciences. The nonlinear Schrödinger equation (NLSE) has been investigated for optical and envelope solitons in various systems, including nonlinear fiber optics, plasma, fluid dynamics, plasmas and cold atoms [1][2][3][4][5][6][7][8][9][10][11]. The NLSE admits many other types of localized structures such as the Peregrine soliton in fibre optics, which is a type of rational solution.…”

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

“…Over the past few years, several efficient analytical techniques for NLEEs have been suggested as the residual power series method [13], Kudryashov's method [14], stability analysis [15], extended $$$ \left({G}^{\prime }/G\right) $$$‐expansion method [16], generalized $$$ \left({G}^{\prime }/G\right) $$$‐expansion method [17], Sardar sub‐equation method [18], advanced exp $$$ \left(-\varphi \left(\xi \right)\right) $$$‐expansion method [19], modified extended tanh‐function method [20], modified Khater method [21], Lie symmetry analysis [22, 23], conservation laws [24], improved Hirota bilinear method [25], generalized exponential rational function method [26, 27], rational sine‐Gordon expansion method [28], extended sinh‐Gordon equation expansion method [29], Adomian decomposition method [30], solitary wave anzatze method [31], $$$ {\exp}_{\alpha } $$$ function method [32], new extended direct algebraic method (NEDAM) [33], extended simple equation method (ESEM) [34], direct algebraic method [35], two‐variable $$$ \left({G}^{\prime }/G;1/G\right) $$$‐expansion approach [36], solitary wave solutions [37], exponential rational function method [38], auxiliary equation mapping method [39], …”

Optical solitons for the decoupled nonlinear Schrödinger equation using Jacobi elliptic approach

“…It's vital to mention that, dynamical systems are usually illustrated in nonlinear complex partial differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Quite a several methods were proposed in the literature to investigate the exact solutions of nonlinear wave problems due to their contributions in describing the physical meaning of different mathematical models see [16][17][18][19][20][21][22][23]. In this work, the Jacobi elliptic scheme [24] is employed to find new soliton solutions of the decoupled nonlinear Schrödinger equation.…”