On optical solitons of the resonant Schrödinger’s equation in optical fibers with dual-power law nonlinearity and time-dependent coefficients

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

“…Several integration schemes have been implemented to examine the behavior of solitons such as ansatz method, semiinverse variational principle, simplest equation approach, first integral method, functional variable method, sine-cosine function method, (G 0 =G)-expansion method, trial solution approach, generalized extended tanh method, modified simple equation method, and improved extended tanh-equation method. For more details, readers are referred to references [14][15][16][17][18][19][20][21][22][23][24][25].…”

Nonlinear Schrödingers equations with cubic nonlinearity: M-derivative soliton solutions by $\exp(-\Phi(\xi))$-Expansion method

“…Thus, investigation of optical soliton with fractional time evolution, become very important due to its application in secure communication system of analog and digital signals, and to carry out hight speed data transmission over distance of several thousands of kilometers [5][6][7][8][9][10][11][12]. Recently, some effective integration methods have been used to construct exact solutions for PDEs, such as semi-inverse variational principe [21], the simplest equation approach [22], the first integral method [23], ansatz scheme [24] and the generalized tanh method [26] and so on. On this way, exact optical solitons in metamaterials with different nonlinearities have been reported [13][14][15].…”

Solitons solutions of nonlinear Schrödinger equation in the left-handed metamaterials by three different techniques

“…It is well known that the partial differential equation (PDEs) of the non-linear Schrodinger equation with hightorder nonlinear terms are near the complex physics phenomena which are concerned many fields from physics to biology etc [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, some effective methods for getting solitons solutions in LHMs and optics has attracted many researchers attention because of soliton theory which is a very important and fascinating area of research in nonlinear left-handed metamaterials and optics.…”

“…Alphonse HOUWE et al obtained solitons of the perturbed nonlinear Schrödingers equation in the nonlinear left-handed transmission lines [18]. In this perspective, many methods for obtaining exact solutions of NLSE was investigated, such as Tan-sech method [10,11], Exponential rational function method [12], the sine-cosine method [13,14], the modified simple equation method [15], and so on.…”