Optical solitons in birefringent fibers with Kaup–Newell equation using two integration schemes

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

“…Jacobi-elliptic function solutions, Weierstrass elliptic function solutions, BSs, dark solitons, singular solitons, and periodic solutions are recovered using these three methods. On comparing our solutions obtained in the present article when the noises 𝜎 𝑗 ( 𝑗 = 1, 2) are nonzero constants with the solutions obtained in Zayed et al [13] when 𝜎 1 = 𝜎 2 = 0, we deduce that the solutions in the present article are more generalization and effective than the solutions obtained in Zayed et al [13]. All solutions of this article have been checked using the Maple by putting them back into Equations (1.1) and (1.2).…”

“…dt to the KNE in birefringent fibers obtained in [11,13] to formulate the above stochastic KNE (1.1) and (1.2) with noise or fluctuations depending on the time t, which have been recognized in many areas via physics, biology, chemistry, and so on. This system models the propagation of the wave through an optical fiber nonlinearity.…”

“…The aspect of stochastically is one of the features that is less touched, and there are a few papers that have discussed this aspect [3][4][5][6][7][8][9]. NLSEs are complex valued evolution equations that play vital roles in many branches of modern science and technology, with the Kaup-Newell equation (KNE) [10][11][12][13][14]. The chirped solitons of the KNE have been studied by the traveling-wave method [10].…”

“…These soliton molecules form the information transporter across intercontinental distances around the world. Lastly, the nonlinear Schrödinger's equation (NLSE) has been discussed with help of many models [1–32, 33–36]. The aspect of stochastically is one of the features that is less touched, and there are a few papers that have discussed this aspect [3–9].…”

“…The analytical and numerical solutions of the KNE have been studied in Al Qarni et al [12]. Direct algebraic method and unified Riccati equation approaches are used to find the optical solitons solutions to KNE [13]. The coupled system derived from the cubic–quartic Kaup–Newell (CQ‐KN) equation in birefringent fiber is described in Zayed et al [14].…”