Modulation instability and solitons on a cw background in inhomogeneous optical fiber media

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

“…By employing the same procedure as in Section 2, we can choose F 1 , G 2 , and F 2 according to (25) - (28) as…”

“…Equation (1) can be transformed into the standard NLSE by means of the similar transformation [24]. Under the conditions Ω (t) = γ(t) = β = const, the N-solitary solution of (1) has been obtained by Darboux transformation [25]. Modulation instability and solitons on a continuouswave background in inhomogeneous optical fiber media have been discussed in [15].…”

Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects

“…Employing the transformation (15) and the Darboux transformation (DT) method [16], and when α 4 = −α 5 , 3α 2 α 3 = α 1 α 4 , one can obtain bright multisolitons for (1):…”

“…The term proportional to f (z) results from the group velocity, g(z) denotes the external electro-optic phase modulation, and h(z) represents the attenuation or absorption coefficient. When f (z) = g(z) = 0, (1) can be extensively used to describe the telecommunication and ultrafast signal-routing systems in the weakly dispersive and nonlinear dielectrics with distributed parameters [12,14,16,17]. If the higher-order terms are ne- (1) degenerates to the vcNLSE [32].…”

Covariant Prolongation Structure, Conservation Laws and Soliton Solutions of the Gross-Pitaevskii Equation in the Bose-Einstein Condensate

“…In the following paper, we plan to investigate the following Gross-Pitaevskii equation in the Bose-Einstein condensate [36] In soliton theory and other fields of science and engineering, the language of technical computing played a very important role in analytically dealing with large amounts of complicated and tedious algebraic calculations [38] [39]. In this paper, we will employ symbolic computation to study the integrability aspects and relevant soliton structures of Gross-Pitaevskii equation in the Bose-Einstein condensate [36] [37].…”