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Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: A dimensional connection.

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Title: Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: A dimensional connection.
Authors: Sun, Yifan1 (AUTHOR) yifan.sun@uniroma1.it, Parra-Rivas, Pedro1 (AUTHOR), Mangini, Fabio1 (AUTHOR), Wabnitz, Stefan1,2 (AUTHOR)
Source: Chaos, Solitons & Fractals. Jun2024, Vol. 183, pN.PAG-N.PAG. 1p.
Subjects: Optical resonators, Linear systems, Structural stability, Potential well, Computational complexity, System dynamics
Abstract: In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations, we transform higher-dimensional models into a single 1D model with a dimension parameter. This transformation not only yields a substantial reduction in computational complexity, but also enables an efficient examination of how dimensionality impacts the system dynamics. In the absence of nonlinearity, we analyze the eigenstates of the linear systems. This allows us to uncover a heightened concentration of the eigenmodes at the center of the potential well, while witnessing a consistent equal spacing among their eigenvalues, as the dimension parameter increases. In the presence of nonlinearity, our findings distinctly reveal that the stability of the localized states diminishes with increasing dimensionality. This study offers an approach to tackling high-dimensional problems, shedding light on the fundamental dimensional connections among radially symmetric states across different dimensions, and providing valuable tools for analysis. [ABSTRACT FROM AUTHOR]
Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: A dimensional connection.
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  Data: <searchLink fieldCode="JN" term="%22Chaos%2C+Solitons+%26+Fractals%22">Chaos, Solitons & Fractals</searchLink>. Jun2024, Vol. 183, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Optical+resonators%22">Optical resonators</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+stability%22">Structural stability</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+well%22">Potential well</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22System+dynamics%22">System dynamics</searchLink>
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  Data: In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations, we transform higher-dimensional models into a single 1D model with a dimension parameter. This transformation not only yields a substantial reduction in computational complexity, but also enables an efficient examination of how dimensionality impacts the system dynamics. In the absence of nonlinearity, we analyze the eigenstates of the linear systems. This allows us to uncover a heightened concentration of the eigenmodes at the center of the potential well, while witnessing a consistent equal spacing among their eigenvalues, as the dimension parameter increases. In the presence of nonlinearity, our findings distinctly reveal that the stability of the localized states diminishes with increasing dimensionality. This study offers an approach to tackling high-dimensional problems, shedding light on the fundamental dimensional connections among radially symmetric states across different dimensions, and providing valuable tools for analysis. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=177315872
RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.chaos.2024.114870
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Optical resonators
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Structural stability
        Type: general
      – SubjectFull: Potential well
        Type: general
      – SubjectFull: Computational complexity
        Type: general
      – SubjectFull: System dynamics
        Type: general
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      – TitleFull: Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: A dimensional connection.
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            NameFull: Sun, Yifan
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            NameFull: Parra-Rivas, Pedro
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            NameFull: Mangini, Fabio
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            NameFull: Wabnitz, Stefan
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            – D: 01
              M: 06
              Text: Jun2024
              Type: published
              Y: 2024
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              Value: 183
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            – TitleFull: Chaos, Solitons & Fractals
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