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Optical soliton resonances and soliton molecules for the Lakshmanan–Porsezian–Daniel system in nonlinear optics

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Abstract

Soliton resonances and soliton molecules play a vital role to generate stable high-energy waves in nonlinear system. Meanwhile, higher-order dispersions and higher-order nonlinearity effects are often introduced in optical models because new optical propagation media have constantly been developed. This article’s motivation is to explore the optical soliton resonances and soliton molecules for the Lakshmanan–Porsezian–Daniel system governed by a four-order nonlinear Schrödinger equation arising in nonlinear optics. Via applying the Darboux transformation method, we obtained the system’s analytical multi-soliton solutions. Then, through managing the spectrum parameters and initial phase parameters, novel soliton resonances and soliton molecules are discovered for the first time to the system. Our study reveals a few of significant properties of the soliton resonances and soliton molecules for the system: (i) The formation mechanism from local soliton resonances to soliton molecules is discovered. The soliton molecules can be established as a limit of local soliton resonances; (ii) the system energy carried by the soliton will obviously increase as local soliton resonances and soliton molecules occur; (iii) the spatiotemporal patterns of soliton molecules will be becoming more complex as the order of soliton solutions increases; (iv) the wave density of soliton molecules will grow with the increase in the weight coefficient of higher-order dispersion and higher-order nonlinearity. These new results indicate that the Lakshmanan–Porsezian–Daniel system may not only generate higher-energy solitons, but also carry richer optical information.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Bang-Qing Li

  2. Academy of Systems Science, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Bang-Qing Li

  3. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Yu-Lan Ma

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  1. Bang-Qing Li
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  2. Yu-Lan Ma
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B-QL was involved in methodology, formal analysis, data curation, writing—original draft. Y-LM helped in conceptualization, software, validation, writing—review and editing, methodology.

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Correspondence to Yu-Lan Ma.

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Li, BQ., Ma, YL. Optical soliton resonances and soliton molecules for the Lakshmanan–Porsezian–Daniel system in nonlinear optics. Nonlinear Dyn 111, 6689–6699 (2023). https://doi.org/10.1007/s11071-022-08195-8

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