Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium

Yuan Shen, Bo Tian, Tian-Yu Zhou and Chong-Dong Cheng

Chaos, Solitons & Fractals, 2023, vol. 171, issue C

Abstract: Investigations on nonlinear optics are active, with the applications in the modulators, fiber lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra-short pulses in an inhomogeneous multi-component nonlinear optical medium. Starting from the existing Lax pair and one-fold Darboux transformation (DT), we construct the N-fold DT of that system, which involves N distinct spectral parameters, where N is a positive integer. The N-fold generalized DT with one spectral parameter is obtained through resorting to the Taylor-series-expansion coefficients of a special solution to that Lax pair. Double-pole soliton solutions of that system are derived via that N-fold generalized DT with N=2. With the aid of the N-fold DT, an N-fold Darboux matrix is constructed, based on which the multi-pole soliton solutions in the determinant form with respect to the electromagnetic field E are determined. Graphically, we find that those double-pole soliton solutions are a kind of the bound-state soliton solutions which represent the elastic interactions between the two solitons. Effects of the coefficients in that system on the double-pole soliton are shown via choosing the trigonometric, linear and quadratic functions. Furthermore, we present the triple-pole soliton and quadruple-pole soliton with respect to E. Our results might be useful in understanding the ultra-short pulses in the nonlinear optical media.

Keywords: Ultra-short pulses; Nonlinear optical medium; N-fold Darboux transformation; N-fold generalized Darboux transformation; Multi-pole soliton (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003983

DOI: 10.1016/j.chaos.2023.113497

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