Singular solitons in optical metamaterials by ansatz method and simplest equation approach

Raman solitons in nanoscale optical waveguides, with metamaterials, having polynomial law non-linearity

“…The factors λ and ν are accounted for self-steepening for preventing shock-waves, and non-linear dispersion. Finally, the terms with θ j for j = 1, 2, 3 arise in the context of optical metamaterials where functional variable method and first integral approach lead to bright and singular 1-soliton solution, as well as continuous waves (4); the ansatz method of integration is employed to extract the 1-soliton solutions and numerical simulations are given to expose the dissipative effects (5); the simplest equation approach also leads to topological soliton, rational solution and singular periodic solution (6); the mapping method is applied to obtain soliton solutions with Kerr and Parabolic law (22); by the aid of collective variables, the numerical simulations of soliton parameter variation are given for specific values of the super-Gaussian pulse parameters (28); a theoretical investigation on the controllability of the Raman soliton self-frequency shift in the metamaterials (31); bright 1-soliton solution is derived by the aid of travelling wave hypothesis in Kerr law, parabolic law and log law non-linearity (33).…”

Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients

“…Some of them are soliton solutions, solitary wave solutions, cnoidal and snoidal waves, periodic solutions, topological soliton solutions as well as various other types, for more references see also . In the nonlinear science, many important phenomena in various fields can be described by NLEEs [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Recently, much attention has been paid to the variable-coefficient nonlinear equations which can describe many nonlinear phenomena more realistically than their constant-coefficient ones.…”

Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method

“…In the literature, many of these methods among which we find are: the Hirotas bilinear method [19], the Backlund transformation method [20], the Darboux transformation method [21], the Painleve singularity structure analysis method [22], the Riccati expansion with constant coefficients [23], the variational iteration method [24], the exp-function method [25], the algebraic method [26], the collocation method [27], the Kudryashov method [28][29][30][31][32], the (G /G)-expansion method [33][34][35][36][37][38], the simplest equation method [39][40][41][42][43], and so on. However, some of these analytical methods are not easy to handle and are often subject to tedious mathematical developments.…”