Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-Lévy-index fractional Kerr media
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929482655334400 |
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| author | Zhong, Ming Chen, Yong Yan, Zhenya Malomed, Boris A. |
| author_facet | Zhong, Ming Chen, Yong Yan, Zhenya Malomed, Boris A. |
| contents | s in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, $α_{1}\, α_{2}\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schrödinger equation with only one Lévy index $α=1$, can be suppressed in the two-Lévy-index fractional nonlinear Schrödinger system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability of continuous waves is investigated in the two-Lévy-index system too. In particular, the modulation instability may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the modulation instability, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-Lévy-index fractional Kerr media Zhong, Ming Chen, Yong Yan, Zhenya Malomed, Boris A. Pattern Formation and Solitons Mathematical Physics Computational Physics Optics Quantum Physics s in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, $α_{1}\, α_{2}\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schrödinger equation with only one Lévy index $α=1$, can be suppressed in the two-Lévy-index fractional nonlinear Schrödinger system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability of continuous waves is investigated in the two-Lévy-index system too. In particular, the modulation instability may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the modulation instability, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity. |
| title | Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-Lévy-index fractional Kerr media |
| topic | Pattern Formation and Solitons Mathematical Physics Computational Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/2409.01135 |