Generation, compression and propagation of pulse trains under higher-order effects

Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: Soliton management

“…(1) under constraints (3), we will employ the Darboux transformation which is an effective procedure and has been widely used to construct soliton solutions of nonlinear Schrödinger equation with variable coefficients [23][24][25].…”

Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source

“…In all these cases, the width and the position of the center of any self-similar wave are specified by Eqs. (10) and (11) and the accumulated phase offset factor C 0 (Z) for β = 1/2 is…”

“…So far, the investigation on optical self-similar waves has been focused on two main issues. The first issue is the discovery of exact self-similar waves, which are mainly described by the exact solitary wave solutions, including bright and dark soliton solutions, quasisoliton solutions, solitary nonlinear Bloch waves, and solitons on the continuous-wave background [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The other is the asymptotic self-similar waves, which are mainly described by the compact parabolic, Hermite, Gaussian, and hybrid functions in which the parabolic self-similar solutions are more intriguing because they can be easily generated from arbitrary input optical waves and retain robustness for the higher initial power [18][19][20][21][22][23][24][25][26].…”

Compression and propagation of dispersive and rectangular similaritons in asymmetric twin-core fibers

“…Self-similar behavior of nonlinear waves is a fundamental property that has been the main focus of study in many areas of physics and, in particular, in optics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In nonlinear optics, the optical similaritons in nonautonomous systems and the asymptotic parabolic similaritons in the gain amplifier systems have been studied extensively due to their potential applications in nonlinearity and dispersion management systems.…”

“…In nonlinear optics, the optical similaritons in nonautonomous systems and the asymptotic parabolic similaritons in the gain amplifier systems have been studied extensively due to their potential applications in nonlinearity and dispersion management systems. Exact optical similaritons are mainly described by exact solitary wave solutions, including bright and dark soliton solutions, quasi-soliton solutions, solitary nonlinear Bloch waves, and the solitons on the continuous wave background [6][7][8][9][10][11][12][13], whose existence requires a delicate balance between the system parameters, such as dispersion, nonlinearity, gain, and inhomogeneity. On the other hand, asymptotic optical similaritons are mainly described by the compact parabolic, Hermite-Gaussian, anGd hybrid functions, in which the parabolic self-similar solutions are more intriguing because they can be easily generated from arbitrary input optical waves and retain their robustness for the higher initial power [14][15][16][17][18].…”