• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.391-398
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• 2024

This article explains how solitons propagate when there is a detuning factor involved. The explanation is based on the nonlinear complex Ginzburg-Landau equation, and we first consider this equation before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on the Ginzburg-Landau equation. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.

• 한국광학회지
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• 제7권4호
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• pp.403-413
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• 1996

We study the propagation of two pulses with orthogonal linear polarizations in a nonlinear periodic dielectric structure with $X^{(3)}$ nonlinearity. Using an envelope- function approach, we derive the coupled nonlinear Schrodinger equations governing the spatio-temporal evolutions of the two orthogonally polarized modes in a nonlinear periodic structure. We then find their solitary-wave solutions referred to as coupled gap solitons. We show that two orthogonally polarized pulses can co-propagate as a coupled gap soliton through a nonlinear periodic structure while each pulse alone will be strongly reflected due to the Bragg reflection. Based on the results, we present an all-optical switching scheme which has a novel architecture and principle. We also study the stability of coupled gap solitons to find the dragging phenomena in a nonlinear birefringent periodic medium.