Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities

Abstract

Communicated by S. GeorgievThe dynamics of dark solitons is studied within the framework of a generalized nonlinear Schrödinger equation. The specific cases of parabolic law and dual-power law nonlinearity are considered. The solitary wave ansatz method is used to carry out the integration. All the physical parameters in the soliton solutions are obtained as functions of the dependent model coefficients. Parametric conditions for the existence of envelope solitons are given.

Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients

“…(3) to the so-called Newwell-Whitehead equation [22,23]. Under these conditions, ( ) can be determined explicitly following to (19) as (25) Note that, in this case, the constants θ 1 θ 2 and θ 3 in (21) will be equal to…”

“…We further report the conditions for the existence of such solutions in terms of the time-dependent model coefficients. The solitary wave ansatz method admits the use of solutions of the form [24][25][26] …”

Optical soliton perturbation with time- and space-dependent dissipation (or gain) and nonlinear dispersion in Kerr and non-Kerr media

“…In recent studies, the non-Kerr law media [7][8][9][10][11][12], such as power law, parabolic law, dual-power law, log law, square-root law, saturating law, exponential law, higher order polynomial law media and so on, have attracted much attention.…”

“…In the nonlinear optics filed, it is well known that the nonlinear Schrödinger equation [1][2][3][4][5][6][7][8][9][10][11][12][13] can be used to describe the propagation of optical pulse in the nonlinear media, including Kerr law and non-Kerr law media. In recent studies, the non-Kerr law media [7][8][9][10][11][12], such as power law, parabolic law, dual-power law, log law, square-root law, saturating law, exponential law, higher order polynomial law media and so on, have attracted much attention.…”

Chirped Optical Solitons in Birefringent Fibers with Parabolic Law Nonlinearity and Four-Wave Mixing

“…The stimulated Raman scattering is due to the delayed response of the medium, which forces the pulse to undergo a frequency shift, known as self-frequency shift [8]. Notice that various types of exact solitons or solitary wave solutions of higher-order NLS-type equations have been studied extensively, both theoretically and numerically [9][10][11][12][13][14][15][16][17]. In particular, a new form of solitary wave solution that takes the shape of W was found for the first time for a single higher-order NLS equation with third-order dispersions, self-steepening, and selffrequency shift effects by Li et al [18].…”