Chirped Waves for a Generalized (2 + 1)-Dimensional Nonlinear Schrödinger Equation

Abstract

The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss).

A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrödinger's Equation with Kerr Law Nonlinearity

“…[27]. In 3D-NLSE case, Lai [28] considered the (2+1)-dimensional generalized NLSE including linear and nonlinear gain (loss) with variable coefficients and obtained the exact chirped soliton-like and quasi-periodic wave solutions. In 4D-NLSE case, Xu et al [29] have generalized the (1+1)D Jacobi elliptic function F-expansion and applied the improved method for solving exact solutions of a generalized (3+1)D NLSE.…”

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“…Employing the transformation (3) and Darboux transformation (DT) [19], one can obtain bright multi-solitons for Eq. ( 1)…”

“…As shown in Fig. 1 (b), another example is the dispersion decreasing fiber (DDF) with the dispersion/diffraction and the nonlinearity parameter [9,19] according to β 1 (z) = β 10 exp(ω 1 z), β 2 (z) = β 20 exp(ω 2 z) and a small constant gain/loss parameter γ = γ 0 . From solutions (23) and ( 24), the initial position and the initial phase of bright soliton pair are related to the parameters θ j0 and φ j0 , while that of dark soliton pair depend on the parameters X j0 and ψ 0 .…”

Multi-soliton solutions to the modified nonlinear Schrödinger equation with variable coefficients in inhomogeneous fibers

“…For reflecting such inhomogeneities influenced by spatial variations of the fiber parameters, the variable coefficient (VC) NLSE serves as a practical model to describe the soliton dynamics, which has been playing a central role in soliton control and dispersion-managed fiber transmission systems [7][8][9][10] since the first soliton dispersion management experiment in a fiber with hyperbolically decreasing GVD was realized by Dianov's group at the General Physics Institute [15]. According to previous studies in nonlinear optics, the VC NLSE can be used to describe not only soliton control [7,8] but also soliton interactions [9,10]. Moreover, many effective mathematical physics methods have been developed to discuss the dynamical behaviors of the optical soliton in inhomogeneous fibers [11][12][13][14].…”

“…Note that these studies [7][8][9][10][11][12][13][14] have not discussed the SS effect for picosecond and shorter pulses, which is due to the intensity dependence of group velocity and forces the peak of the pulse to travel slower than the wings, causing an asymmetrical spectral broadening of the pulse [16]. Considering this effect, we pay attention to the following modified VC NLSE [18]:…”